Not able to correct the sign of computed SVD.

I am trying to check the working of Matlab's SVD by correcting the sign of the computed SVD.

Step 1: I am creating an A matrix from random U,S and V' ;

Step 2: I am calculating the svd(A) and finding subsequent U2,S2 and V2'

Step 3: Next up I am comparing the U, V and A by taking the norm of their difference!

Step 4: Correction step; I am multiplying the computed U2, V2 with appropriate sign changes such that they get back to the original sign convention.

Step 5: I am again comparing them with original U,V and A in N4,N5 and N6!

The U matrix is getting corrected but the V and A matrix is still showing error of high orders! Can anyone help me with this!

Thanks!

U = rand(50);
V = rand(50);
d = rand(50,1);
s = sort(d);
S = diag(d);

A = U*S*(V)'; % Compute A matrix from U, S, V

[U2,S2,V2]= svd(A); % Compute SVD of A
A2 = U2*S2*(V2)';

N1=norm(U2-U);
N2=norm(V2-V);
N3= norm(A2-A);

D = ((U2')*U); % Converting to diagonal matrix for plotting only
D2 = ((V2')*V);

A3 = (U2*D)*S2*(D2*V2)';

N4=norm(U2*D-U);
N5=norm(D2*V2-V);
N6 = norm(A3-A);

[Torsten]

I see nowhere that the U and V you use are unitary matrices.

[Anshuman]

How to do that? How to assign unitary matrix instead of a random one?

[Anshuman]

Hey I got it corrected; thanks a lot! I took [U,R1] = qr(U) and [V,R2] = qr(V)!

[Torsten]

Did you ask google ? There are so many hits for "matlab & generate unitary matrix".

[Anshuman]

Naah, I figured it out from my linear algebra class! Thanks!