How to get roots of determinant (characteristic) equation?

Question

Amit Kumar 2014-4-30

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https://ww2.mathworks.cn/matlabcentral/answers/127679-how-to-get-roots-of-determinant-characteristic-equation

评论： Walter Roberson 2021-10-4

Hello all, I am solving an eigenvalue problem and giving symbolic matrix as input. I want to find roots of characteristic equation, I mean, roots of determinant of matrix equated to zero. Here I give script:

clear all;
close all;
clc;
syms w
A=[-2000*w^2+280*1e3,-280*1e3;280*1e3,-2000*w^2+280*1e3];
fun = matlabFunction(det(A))

I want to find roots of fun(). This is a polynomial equation of 4th order, so I should have 4 roots. If I use fzero, it just gives a local solution to problem, but I want to have all roots. Can you suggest something? Ofcourse, I can write coefficients of det(A) manually and pass it to roots([...]). But I don't want to write manually. I am even trying to bypass symbolics, as for large matrix, symbolic variables are computationally very expensive. Any comments? Thanks in advance!

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Answer 1

Star Strider 2014-4-30

3
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https://ww2.mathworks.cn/matlabcentral/answers/127679-how-to-get-roots-of-determinant-characteristic-equation#answer_135103

编辑：Star Strider 2014-4-30

在 MATLAB Online 中打开

Use the Symbolic Math Toolbox solve function:

DA = det(A)
W = solve(DA,w)

produces:

W =
    (140 + 140*i)^(1/2)
    (140 - 140*i)^(1/2)
   -(140 + 140*i)^(1/2)
   -(140 - 140*i)^(1/2)

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Amit Kumar 2014-4-30

Thanks a lot!!!

Star Strider 2014-4-30

My pleasure!

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Answer 2

Pratik Baraiya 2021-10-4

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/127679-how-to-get-roots-of-determinant-characteristic-equation#answer_800874

在 MATLAB Online 中打开

clear all;
close all;
clc;
syms w
A=[-2000*w^2+280*1e3,-280*1e3;280*1e3,-2000*w^2+280*1e3];
fun = matlabFunction(det(A))
fun = function_handle with value:
    @(w)w.^2.*-1.12e+9+w.^4.*4.0e+6+1.568e+11