# How to get roots of determinant (characteristic) equation?

44 views (last 30 days)
Amit Kumar on 30 Apr 2014
Commented: Walter Roberson on 4 Oct 2021
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!

Star Strider on 30 Apr 2014
Edited: Star Strider on 30 Apr 2014
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)
Star Strider on 30 Apr 2014
My pleasure!

Pratik Baraiya on 4 Oct 2021
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
Walter Roberson on 4 Oct 2021
What is your recommendation to proceed from fun to find the roots of fun ?

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