12/22/2023 0 Comments Matlab eig% eigenvectors of A*A' are the same as the left-singular vectors % eigenvectors of A'*A are the same as the right-singular vectors Note that svd and eig return results in different order (one sorted high to low, the other in reverse): % some random matrix Now as you know, SVD and eigendecomposition are related. MATLAB chooses to normalize the eigenvectors to have a norm of 1.0, the sign is arbitrary:įor eig(A), the eigenvectors are scaled so that the norm of each is 1.0.įor eig(A,B), eig(A,'nobalance'), and eig(A,B,flag), the eigenvectors are not normalized This is clear given the definition of an eigenvector: A Multiplying by any constant, including -1 (which simply changes the sign), gives another valid eigenvector. obviously if t is an eigenvector, then also -t is an eigenvector, but with the signs inverted (for some of the columns, not all) I don't get A = U * S * V'.Įxample: for the matrix A= my function returns: U=Īnd the built-in MATLAB svd function returns: u= But some of the columns are multiplied by -1. My code returns the correct s matrix, and also "nearly" correct U and V matrices. Problem is: the MATLAB function eig sometimes returns the wrong eigenvectors. Where A is the matrix the user enters, U is an orthogonal matrix composes of the eigenvectors of A * A', S is a diagonal matrix of the singular values, and V is an orthogonal matrix of the eigenvectors of A' * A. I'm trying to write a program that gets a matrix A of any size, and SVD decomposes it: A = U * S * V'
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