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Find the eigenvectors and eigenvalues of the following matrix in MATLAB:
MATLAB can compute eigenvalues and eigenvectors of a square matrix, either numerically or symbolically.
Numerical eigenvalues and eigenvectors
(Note: green color marks user input, and blue color is MATLAB response.)
First let’s set matrix:
A = [3 2 4; 2 0 2; 4 2 3]
The “eig” command computes the eigenvalues and eigenvectors:
[V,D] = eig(A)
The “eig” command returns two matrices. The first contains the eigenvectors as the columns of the matrix, while the second is a diagonal matrix with the eigenvalues on the diagonal. The eigenvectors and eigenvalues are given in the same order.
We can also call the “eig” command with a single output, in which case only the eigenvalues are returned, and in a vector instead of a matrix:
ev = eig(A)
Symbolical eigenvalues and eigenvectors
To obtain symbolic (exact) eigenvalues and eigenvectors, it is only necessary to define the matrix to be symbolic:
The computation then proceeds exactly as before: