# how can i find matrix spectral decomposition in matlab

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Israa on 16 Mar 2024
Commented: Torsten on 17 Mar 2024
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?

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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Israa on 17 Mar 2024
Thanks but is there a way i can directly use the spectralfact function?
Torsten on 17 Mar 2024
Yes, by licencing the Control System Toolbox.

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