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how can i find matrix spectral decomposition in matlab

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im trying to find spectral decomposition for H = [1 2; 2 -1] using [G,S] = spectralfact(H); but i get this message spectralfact requires Control System Toolbox. i tried clicking on the link for the toolbox but i cant find somthing helpful. what should i do?

Accepted Answer

Hassaan on 17 Mar 2024
Edited: Hassaan on 17 Mar 2024
If you can't get access to the Control System Toolbox, you can manually perform spectral decomposition for a 2x2 matrix like H = [1 2; 2 -1] using basic MATLAB commands, since the spectral decomposition is essentially finding the eigenvalues and eigenvectors of the matrix.
H = [1 2; 2 -1];
% Compute the eigenvalues and eigenvectors
[V, D] = eig(H);
% V contains the eigenvectors, D contains the eigenvalues on the diagonal
% The columns of V are the eigenvectors and the diagonal elements of D are the corresponding eigenvalues
% The matrix G here is V, and S is D in the spectral decomposition formula H = V*D*V'
G = V;
S = D;
% Display the results
G, S
G = 2×2
0.5257 -0.8507 -0.8507 -0.5257
S = 2×2
-2.2361 0 0 2.2361
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It's important to note that the advice and code are based on limited information and meant for educational purposes. Users should verify and adapt the code to their specific needs, ensuring compatibility and adherence to ethical standards.
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Israa on 17 Mar 2024
Thanks but is there a way i can directly use the spectralfact function?

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