Numerical value of Determinant far from what it is supposed to beNumeric values from transformFindRoot for numerical function and how to search more than one rootCan't get a numerical value for this vector operationNumerical value of an expression with a uniform step sizeNumerical evaluation after Normal?Numerical Results with replacement rulesStrange numerical valuesWhat is the acceptable error in numerical calculations?High numerical precision failingHow to extract the minimal value from NMinimize?

What does *dead* mean in *What do you mean, dead?*?

Having the player face themselves after the mid-game

The (Easy) Road to Code

If nine coins are tossed, what is the probability that the number of heads is even?

Why do we say 'Pairwise Disjoint', rather than 'Disjoint'?

What will happen if my luggage gets delayed?

Do Cubics always have one real root?

ESPP--any reason not to go all in?

Translation of 答えを知っている人はいませんでした

Short scifi story where reproductive organs are converted to produce "materials", pregnant protagonist is "found fit" to be a mother

Can't make sense of a paragraph from Lovecraft

What do you call someone who likes to pick fights?

Movie: boy escapes the real world and goes to a fantasy world with big furry trolls

Why restrict private health insurance?

(Codewars) Linked Lists-Sorted Insert

Does an unused member variable take up memory?

Rationale to prefer local variables over instance variables?

Difference between `nmap local-IP-address` and `nmap localhost`

Use Mercury as quenching liquid for swords?

Smooth vector fields on a surface modulo diffeomorphisms

Why is there an extra space when I type "ls" on the Desktop?

Can I take the the bonus-action attack from Two-Weapon Fighting without taking the Attack action?

Can one live in the U.S. and not use a credit card?

Locked Away- What am I?



Numerical value of Determinant far from what it is supposed to be


Numeric values from transformFindRoot for numerical function and how to search more than one rootCan't get a numerical value for this vector operationNumerical value of an expression with a uniform step sizeNumerical evaluation after Normal?Numerical Results with replacement rulesStrange numerical valuesWhat is the acceptable error in numerical calculations?High numerical precision failingHow to extract the minimal value from NMinimize?













1












$begingroup$


I have a large matrix with numerical components and want to set the determinant to zero using the parameter h (see below). Naively, I would have expected that h sets the determinant to (approximately) zero, which isn't the case. On top of that, the order of applying the rule sol seems to affects the final outcome for a reason to don't see.



My output of the code below is:



h -> -0.744736 + 4.42008 I

0.0445865 - 0.0285418 I

0.0545654 - 0.114258 I


I am not familiar with how Mathematica handles floating point numbers so that's probably where my error lies. I have also tried to increase the precision with SetPrecision, but without success.



mat=0.16 - (0.36 + 0.001 I) h - (1.35808 - 
 0.00120116 I) h^2 - (0.49603 - 0.00137214 I) h^3 - (0.11307 - 
 0.00105331 I) h^4 + (0.249794 - 0.000384238 I) h^5 - 
0.39204 h^6, -0.1711 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h - (1.15528 + 
 0.00267142 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 
 1. h^4), (0.0000353051 - 1.67323*10^-6 I) h^4, 
0, -0.1711 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (19.6394 - 
 0.00267142 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 1. h^4), 
0.16 - (0.36 + 0.001 I) h - (11.3534 - 
 0.00119507 I) h^2 - (0.484268 - 0.00140481 I) h^3 - (5.0714 - 
 0.00114074 I) h^4 + (0.27061 - 0.000416258 I) h^5 - 
0.42471 h^6, -0.223386 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (4.95742 - 
 0.00267502 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 
 1. h^4), (0.0000484431 - 2.29589*10^-6 I) h^4, (0.0000353051 - 
 1.67323*10^-6 I) h^4, -0.223386 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (41.4016 - 
 0.00267502 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 1. h^4), 
0.16 - (0.36 + 0.001 I) h - (29.348 - 
 0.00118803 I) h^2 - (0.470698 - 0.00144251 I) h^3 - (13.9095 - 
 0.00124106 I) h^4 + (0.294629 - 0.000453204 I) h^5 - 
0.462406 h^6, -0.234771 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (19.0123 - 
 0.00267319 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 
 1. h^4), 0, (0.0000484431 - 
 2.29589*10^-6 I) h^4, -0.234771 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (71.32 - 
 0.00267319 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 1. h^4), 
0.16 - (0.36 + 0.001 I) h - (55.3462 - 
 0.00118568 I) h^2 - (0.466163 - 0.0014551 I) h^3 - (26.6556 - 
 0.00127449 I) h^4 + (0.302655 - 0.000465551 I) h^5 - 
0.475003 h^6;
sol = Part[NSolve[Det[%] == 0, h], 1]
Det[mat /. sol]
Det[mat] /. sol





numerical-value







share|improve this question







New contributor




Nils is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$











  • $begingroup$
    Correction: I get the output 0.118714 - 0.0526506 I (as the second output) and 0.106201 - 0.0979004 I (as the third output); sorry, used a different matrix. But the problem still stands.
    $endgroup$
    – Nils
    2 hours ago















1












$begingroup$


I have a large matrix with numerical components and want to set the determinant to zero using the parameter h (see below). Naively, I would have expected that h sets the determinant to (approximately) zero, which isn't the case. On top of that, the order of applying the rule sol seems to affects the final outcome for a reason to don't see.



My output of the code below is:



h -> -0.744736 + 4.42008 I

0.0445865 - 0.0285418 I

0.0545654 - 0.114258 I


I am not familiar with how Mathematica handles floating point numbers so that's probably where my error lies. I have also tried to increase the precision with SetPrecision, but without success.



mat=0.16 - (0.36 + 0.001 I) h - (1.35808 - 
 0.00120116 I) h^2 - (0.49603 - 0.00137214 I) h^3 - (0.11307 - 
 0.00105331 I) h^4 + (0.249794 - 0.000384238 I) h^5 - 
0.39204 h^6, -0.1711 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h - (1.15528 + 
 0.00267142 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 
 1. h^4), (0.0000353051 - 1.67323*10^-6 I) h^4, 
0, -0.1711 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (19.6394 - 
 0.00267142 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 1. h^4), 
0.16 - (0.36 + 0.001 I) h - (11.3534 - 
 0.00119507 I) h^2 - (0.484268 - 0.00140481 I) h^3 - (5.0714 - 
 0.00114074 I) h^4 + (0.27061 - 0.000416258 I) h^5 - 
0.42471 h^6, -0.223386 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (4.95742 - 
 0.00267502 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 
 1. h^4), (0.0000484431 - 2.29589*10^-6 I) h^4, (0.0000353051 - 
 1.67323*10^-6 I) h^4, -0.223386 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (41.4016 - 
 0.00267502 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 1. h^4), 
0.16 - (0.36 + 0.001 I) h - (29.348 - 
 0.00118803 I) h^2 - (0.470698 - 0.00144251 I) h^3 - (13.9095 - 
 0.00124106 I) h^4 + (0.294629 - 0.000453204 I) h^5 - 
0.462406 h^6, -0.234771 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (19.0123 - 
 0.00267319 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 
 1. h^4), 0, (0.0000484431 - 
 2.29589*10^-6 I) h^4, -0.234771 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (71.32 - 
 0.00267319 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 1. h^4), 
0.16 - (0.36 + 0.001 I) h - (55.3462 - 
 0.00118568 I) h^2 - (0.466163 - 0.0014551 I) h^3 - (26.6556 - 
 0.00127449 I) h^4 + (0.302655 - 0.000465551 I) h^5 - 
0.475003 h^6;
sol = Part[NSolve[Det[%] == 0, h], 1]
Det[mat /. sol]
Det[mat] /. sol





numerical-value







share|improve this question







New contributor




Nils is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$











  • $begingroup$
    Correction: I get the output 0.118714 - 0.0526506 I (as the second output) and 0.106201 - 0.0979004 I (as the third output); sorry, used a different matrix. But the problem still stands.
    $endgroup$
    – Nils
    2 hours ago













1












1








1





$begingroup$


I have a large matrix with numerical components and want to set the determinant to zero using the parameter h (see below). Naively, I would have expected that h sets the determinant to (approximately) zero, which isn't the case. On top of that, the order of applying the rule sol seems to affects the final outcome for a reason to don't see.



My output of the code below is:



h -> -0.744736 + 4.42008 I

0.0445865 - 0.0285418 I

0.0545654 - 0.114258 I


I am not familiar with how Mathematica handles floating point numbers so that's probably where my error lies. I have also tried to increase the precision with SetPrecision, but without success.



mat=0.16 - (0.36 + 0.001 I) h - (1.35808 - 
 0.00120116 I) h^2 - (0.49603 - 0.00137214 I) h^3 - (0.11307 - 
 0.00105331 I) h^4 + (0.249794 - 0.000384238 I) h^5 - 
0.39204 h^6, -0.1711 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h - (1.15528 + 
 0.00267142 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 
 1. h^4), (0.0000353051 - 1.67323*10^-6 I) h^4, 
0, -0.1711 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (19.6394 - 
 0.00267142 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 1. h^4), 
0.16 - (0.36 + 0.001 I) h - (11.3534 - 
 0.00119507 I) h^2 - (0.484268 - 0.00140481 I) h^3 - (5.0714 - 
 0.00114074 I) h^4 + (0.27061 - 0.000416258 I) h^5 - 
0.42471 h^6, -0.223386 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (4.95742 - 
 0.00267502 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 
 1. h^4), (0.0000484431 - 2.29589*10^-6 I) h^4, (0.0000353051 - 
 1.67323*10^-6 I) h^4, -0.223386 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (41.4016 - 
 0.00267502 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 1. h^4), 
0.16 - (0.36 + 0.001 I) h - (29.348 - 
 0.00118803 I) h^2 - (0.470698 - 0.00144251 I) h^3 - (13.9095 - 
 0.00124106 I) h^4 + (0.294629 - 0.000453204 I) h^5 - 
0.462406 h^6, -0.234771 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (19.0123 - 
 0.00267319 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 
 1. h^4), 0, (0.0000484431 - 
 2.29589*10^-6 I) h^4, -0.234771 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (71.32 - 
 0.00267319 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 1. h^4), 
0.16 - (0.36 + 0.001 I) h - (55.3462 - 
 0.00118568 I) h^2 - (0.466163 - 0.0014551 I) h^3 - (26.6556 - 
 0.00127449 I) h^4 + (0.302655 - 0.000465551 I) h^5 - 
0.475003 h^6;
sol = Part[NSolve[Det[%] == 0, h], 1]
Det[mat /. sol]
Det[mat] /. sol





numerical-value







share|improve this question







New contributor




Nils is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




I have a large matrix with numerical components and want to set the determinant to zero using the parameter h (see below). Naively, I would have expected that h sets the determinant to (approximately) zero, which isn't the case. On top of that, the order of applying the rule sol seems to affects the final outcome for a reason to don't see.



My output of the code below is:



h -> -0.744736 + 4.42008 I

0.0445865 - 0.0285418 I

0.0545654 - 0.114258 I


I am not familiar with how Mathematica handles floating point numbers so that's probably where my error lies. I have also tried to increase the precision with SetPrecision, but without success.



mat=0.16 - (0.36 + 0.001 I) h - (1.35808 - 
 0.00120116 I) h^2 - (0.49603 - 0.00137214 I) h^3 - (0.11307 - 
 0.00105331 I) h^4 + (0.249794 - 0.000384238 I) h^5 - 
0.39204 h^6, -0.1711 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h - (1.15528 + 
 0.00267142 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 
 1. h^4), (0.0000353051 - 1.67323*10^-6 I) h^4, 
0, -0.1711 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (19.6394 - 
 0.00267142 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 1. h^4), 
0.16 - (0.36 + 0.001 I) h - (11.3534 - 
 0.00119507 I) h^2 - (0.484268 - 0.00140481 I) h^3 - (5.0714 - 
 0.00114074 I) h^4 + (0.27061 - 0.000416258 I) h^5 - 
0.42471 h^6, -0.223386 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (4.95742 - 
 0.00267502 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 
 1. h^4), (0.0000484431 - 2.29589*10^-6 I) h^4, (0.0000353051 - 
 1.67323*10^-6 I) h^4, -0.223386 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (41.4016 - 
 0.00267502 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 1. h^4), 
0.16 - (0.36 + 0.001 I) h - (29.348 - 
 0.00118803 I) h^2 - (0.470698 - 0.00144251 I) h^3 - (13.9095 - 
 0.00124106 I) h^4 + (0.294629 - 0.000453204 I) h^5 - 
0.462406 h^6, -0.234771 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (19.0123 - 
 0.00267319 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 
 1. h^4), 0, (0.0000484431 - 
 2.29589*10^-6 I) h^4, -0.234771 h^2 ((-0.143205 + 
 0.000186623 I) - (0.36 + 0.001 I) h + (71.32 - 
 0.00267319 I) h^2 - (0.637164 - 0.0009801 I) h^3 + 1. h^4), 
0.16 - (0.36 + 0.001 I) h - (55.3462 - 
 0.00118568 I) h^2 - (0.466163 - 0.0014551 I) h^3 - (26.6556 - 
 0.00127449 I) h^4 + (0.302655 - 0.000465551 I) h^5 - 
0.475003 h^6;
sol = Part[NSolve[Det[%] == 0, h], 1]
Det[mat /. sol]
Det[mat] /. sol





numerical-value




numerical-value






share|improve this question







New contributor




Nils is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question







New contributor




Nils is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question






New contributor




Nils is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 2 hours ago









NilsNils

61




61




New contributor




Nils is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Nils is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Nils is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











  • $begingroup$
    Correction: I get the output 0.118714 - 0.0526506 I (as the second output) and 0.106201 - 0.0979004 I (as the third output); sorry, used a different matrix. But the problem still stands.
    $endgroup$
    – Nils
    2 hours ago
















  • $begingroup$
    Correction: I get the output 0.118714 - 0.0526506 I (as the second output) and 0.106201 - 0.0979004 I (as the third output); sorry, used a different matrix. But the problem still stands.
    $endgroup$
    – Nils
    2 hours ago















$begingroup$
Correction: I get the output 0.118714 - 0.0526506 I (as the second output) and 0.106201 - 0.0979004 I (as the third output); sorry, used a different matrix. But the problem still stands.
$endgroup$
– Nils
2 hours ago




$begingroup$
Correction: I get the output 0.118714 - 0.0526506 I (as the second output) and 0.106201 - 0.0979004 I (as the third output); sorry, used a different matrix. But the problem still stands.
$endgroup$
– Nils
2 hours ago










1 Answer
1






active

oldest

votes


















3












$begingroup$

As you suspected when you mentioned SetPrecision, you are encountering numerical errors, probably catastrophic loss of precision when calculating the determinant; your calculations do in fact need to be carried out at higher precision.



If possible, you would want to use exact numbers in your matrix, or take advantage of the arbitrary-precision capabilities of Mathematica. For instance, we can convert all machine-precision numbers to arbitrary-precision ones with a number of digits of precision equal to that of common machine-precision numbers on your machine using SetPrecision (see also $MachinePrecision in the documentation):



det = Det[SetPrecision[mat, $MachinePrecision]];
sol = NSolve[det == 0, h];
det /. sol // PossibleZeroQ

(* Out: 
 True, True, True, True, True, True, True, True, True, True, True,
 True, True, True, True, True, True, True, True, True, True, True,
 True, True 
*)


As you can see, all those values of $h$ do bring your determinant reasonably close to zero, within machine-precision approximations.






share|improve this answer











$endgroup$












    Your Answer





    StackExchange.ifUsing("editor", function ()
    return StackExchange.using("mathjaxEditing", function ()
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    );
    );
    , "mathjax-editing");

    StackExchange.ready(function()
    var channelOptions =
    tags: "".split(" "),
    id: "387"
    ;
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function()
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled)
    StackExchange.using("snippets", function()
    createEditor();
    );

    else
    createEditor();

    );

    function createEditor()
    StackExchange.prepareEditor(
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: false,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: null,
    bindNavPrevention: true,
    postfix: "",
    imageUploader:
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    ,
    onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    );



    );






    Nils is a new contributor. Be nice, and check out our Code of Conduct.









    draft saved

    draft discarded


















    StackExchange.ready(
    function ()
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f192970%2fnumerical-value-of-determinant-far-from-what-it-is-supposed-to-be%23new-answer', 'question_page');

    );

    Post as a guest















    Required, but never shown

























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    3












    $begingroup$

    As you suspected when you mentioned SetPrecision, you are encountering numerical errors, probably catastrophic loss of precision when calculating the determinant; your calculations do in fact need to be carried out at higher precision.



    If possible, you would want to use exact numbers in your matrix, or take advantage of the arbitrary-precision capabilities of Mathematica. For instance, we can convert all machine-precision numbers to arbitrary-precision ones with a number of digits of precision equal to that of common machine-precision numbers on your machine using SetPrecision (see also $MachinePrecision in the documentation):



    det = Det[SetPrecision[mat, $MachinePrecision]];
    sol = NSolve[det == 0, h];
    det /. sol // PossibleZeroQ

    (* Out: 
     True, True, True, True, True, True, True, True, True, True, True,
     True, True, True, True, True, True, True, True, True, True, True,
     True, True 
    *)


    As you can see, all those values of $h$ do bring your determinant reasonably close to zero, within machine-precision approximations.






    share|improve this answer











    $endgroup$

















      3












      $begingroup$

      As you suspected when you mentioned SetPrecision, you are encountering numerical errors, probably catastrophic loss of precision when calculating the determinant; your calculations do in fact need to be carried out at higher precision.



      If possible, you would want to use exact numbers in your matrix, or take advantage of the arbitrary-precision capabilities of Mathematica. For instance, we can convert all machine-precision numbers to arbitrary-precision ones with a number of digits of precision equal to that of common machine-precision numbers on your machine using SetPrecision (see also $MachinePrecision in the documentation):



      det = Det[SetPrecision[mat, $MachinePrecision]];
      sol = NSolve[det == 0, h];
      det /. sol // PossibleZeroQ

      (* Out: 
       True, True, True, True, True, True, True, True, True, True, True,
       True, True, True, True, True, True, True, True, True, True, True,
       True, True 
      *)


      As you can see, all those values of $h$ do bring your determinant reasonably close to zero, within machine-precision approximations.






      share|improve this answer











      $endgroup$















        3












        3








        3





        $begingroup$

        As you suspected when you mentioned SetPrecision, you are encountering numerical errors, probably catastrophic loss of precision when calculating the determinant; your calculations do in fact need to be carried out at higher precision.



        If possible, you would want to use exact numbers in your matrix, or take advantage of the arbitrary-precision capabilities of Mathematica. For instance, we can convert all machine-precision numbers to arbitrary-precision ones with a number of digits of precision equal to that of common machine-precision numbers on your machine using SetPrecision (see also $MachinePrecision in the documentation):



        det = Det[SetPrecision[mat, $MachinePrecision]];
        sol = NSolve[det == 0, h];
        det /. sol // PossibleZeroQ

        (* Out: 
         True, True, True, True, True, True, True, True, True, True, True,
         True, True, True, True, True, True, True, True, True, True, True,
         True, True 
        *)


        As you can see, all those values of $h$ do bring your determinant reasonably close to zero, within machine-precision approximations.






        share|improve this answer











        $endgroup$



        As you suspected when you mentioned SetPrecision, you are encountering numerical errors, probably catastrophic loss of precision when calculating the determinant; your calculations do in fact need to be carried out at higher precision.



        If possible, you would want to use exact numbers in your matrix, or take advantage of the arbitrary-precision capabilities of Mathematica. For instance, we can convert all machine-precision numbers to arbitrary-precision ones with a number of digits of precision equal to that of common machine-precision numbers on your machine using SetPrecision (see also $MachinePrecision in the documentation):



        det = Det[SetPrecision[mat, $MachinePrecision]];
        sol = NSolve[det == 0, h];
        det /. sol // PossibleZeroQ

        (* Out: 
         True, True, True, True, True, True, True, True, True, True, True,
         True, True, True, True, True, True, True, True, True, True, True,
         True, True 
        *)


        As you can see, all those values of $h$ do bring your determinant reasonably close to zero, within machine-precision approximations.







        share|improve this answer














        share|improve this answer



        share|improve this answer








        edited 2 hours ago

























        answered 2 hours ago









        MarcoBMarcoB

        37.3k556113




        37.3k556113




















            Nils is a new contributor. Be nice, and check out our Code of Conduct.









            draft saved

            draft discarded


















            Nils is a new contributor. Be nice, and check out our Code of Conduct.












            Nils is a new contributor. Be nice, and check out our Code of Conduct.











            Nils is a new contributor. Be nice, and check out our Code of Conduct.














            Thanks for contributing an answer to Mathematica Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid …


            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.

            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function ()
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f192970%2fnumerical-value-of-determinant-far-from-what-it-is-supposed-to-be%23new-answer', 'question_page');

            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            -

            Popular posts from this blog

            Frič See also Navigation menuinternal link

            Image
            SurnamesCzech-language surnames ‹ The template Infobox surname is being considered for merging. › Frič Origin Language(s) Czechized German (eastern Middle German dialects and Alemannic German) - Thuringian, Upper Saxon, Low Lusatian, Silesian Meaning derived from German: Friedrich Other names Variant(s) Fritsch, Fritzsch, Frycz, Fricz, Fryczyński, Frietsch, Fritsche, Fritzsche; Fritschi (Alemannic), Fritz, Fritze, Fritzel, Fritzl, Fritzke, Fritzen Frič is a Czechized German surname. Notable people with the surname include: Alberto Vojtěch Frič, Czech botanist Antonín Jan Frič (Fritsch) , Czech paleontologist Jaroslav Erik Frič, Czech poet Martin Frič, Czech film director, screenwriter and actor See also Fričovce (Hungarian: Frics ) .mw-parser-output table.dmboxclear:both;margin:0.9em 1em;border-top:1px solid #ccc;border-bottom:1px solid #ccc;background-color:transparent Surname list This page lists people with...
            Read more

            Identify plant with long narrow paired leaves and reddish stems Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern) Announcing the arrival of Valued Associate #679: Cesar Manara Unicorn Meta Zoo #1: Why another podcast?What is this plant with long sharp leaves? Is it a weed?What is this 3ft high, stalky plant, with mid sized narrow leaves?What is this young shrub with opposite ovate, crenate leaves and reddish stems?What is this plant with large broad serrated leaves?Identify this upright branching weed with long leaves and reddish stemsPlease help me identify this bulbous plant with long, broad leaves and white flowersWhat is this small annual with narrow gray/green leaves and rust colored daisy-type flowers?What is this chilli plant?Does anyone know what type of chilli plant this is?Help identify this plant

            Image
            Apollo command module space walk? prime numbers and expressing non-prime numbers Can a non-EU citizen traveling with me come with me through the EU passport line? Extract all GPU name, model and GPU ram How to deal with a team lead who never gives me credit? Why was the term "discrete" used in discrete logarithm? Why do we bend a book to keep it straight? When do you get frequent flier miles - when you buy, or when you fly? How come Sam didn't become Lord of Horn Hill? At the end of Thor: Ragnarok why don't the Asgardians turn and head for the Bifrost as per their original plan? Is it true that "carbohydrates are of no use for the basal metabolic need"? Using et al. for a last / senior author rather than for a first author How to tell that you are a giant? How to react to hostile behavior from a senior developer? String `!23` is replaced with `docker` in command line How to find out what spells would be useless to a blind NPC sp...
            Read more

            fontconfig warning: “/etc/fonts/fonts.conf”, line 100: unknown “element blank” The 2019 Stack Overflow Developer Survey Results Are In“tar: unrecognized option --warning” during 'apt-get install'How to fix Fontconfig errorHow do I figure out which font file is chosen for a system generic font alias?Why are some apt-get-installed fonts being ignored by fc-list, xfontsel, etc?Reload settings in /etc/fonts/conf.dTaking 30 seconds longer to boot after upgrade from jessie to stretchHow to match multiple font names with a single <match> element?Adding a custom font to fontconfigRemoving fonts from fontconfig <match> resultsBroken fonts after upgrading Firefox ESR to latest Firefox

            Image
            How to type this arrow in math mode? Multiply Two Integer Polynomials What do hard-Brexiteers want with respect to the Irish border? Why isn't the circumferential light around the M87 black hole's event horizon symmetric? For what reasons would an animal species NOT cross a *horizontal* land bridge? Can one be advised by a professor who is very far away? Identify boardgame from Big movie slides for 30min~1hr skype tenure track application interview Why do we hear so much about the Trump administration deciding to impose and then remove tariffs? If I score a critical hit on an 18 or higher, what are my chances of getting a critical hit if I roll 3d20? Can we generate random numbers using irrational numbers like π and e? Worn-tile Scrabble Output the Arecibo Message What is the meaning of Triage in Cybersec world? How are circuits which use complex ICs normally simulated? Shouldn't "much" here be used instead of "more"? Dele...
            Read more