Singular value decomposition : svd

svd (singular value decomposition) takes as argument a numeric square matrix of size n.
svd(A) returns an orthogonal matrix U, the diagonal s of a diagonal matrix S and an orthogonal matrix Q (^tQ*Q = I) such that :

A = U.S.^tQ

Input :

svd([[1,2],[3,4]])

Output :

[[-0.404553584834,-0.914514295677],[-0.914514295677, 0.404553584834]], [5.46498570422,0.365966190626], [[-0.576048436766,0.81741556047],[-0.81741556047, -0.576048436766]]

Input :

(U,s,Q):=svd([[3,5],[4,5]])

Output :

[[-0.672988041811,-0.739653361771],[-0.739653361771, 0.672988041811]],[8.6409011028,0.578643354497], [[-0.576048436766,0.81741556047],[-0.81741556047, -0.576048436766]]

Verification : Input :

U*diag(s)*tran(Q)

Output :

[[3.0,5.0],[4.0,5.0]]