# Vectorizing diagonalization of multiple matrices

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## Vectorizing diagonalization of multiple matrices

 I have a matrix M which is a function of two variables, x and y, and I want to diagonalize it for many pairs of x and y. If I index x as x(u) and y as y(v), then I can write the elements of the matrix as M(i,j,u,v) where i and j index which element of the matrix.Currently I am constructing and diagonalizing the matrices with for loops:x = linspace(0,1,5); y = linspace(2,3,5); for u=1:5for v=1:5 M = [ y(v)*x(u) , x(u) ;  x(u) , -y(v)^2 ]; [vecs(:,:,u,v),vals (:,:,u,v)] = eig(M(:,:,u,v));endendI've been able to vectorize almost all the rest of my code, and this is the last part. Is there a way to vectorize this? My experience with vectorization is fairly limited, so please let me know if you have any side comments on this - for example, whether vectorization would actually speed it up.I should add that although my MWE is a 2x2, I would in practice be doing this with a 4x4 matrix, if that is relevant to whether or not vectorizing the diagonalization would actually do much to accelerate my code.- Brett Green