how to generate a random matrix with Orthogonalized rows using Gram-Schmidt algorithm in Matlab

Question

I want to generate a M*N matrix (M is not equal to N) with following constraints in MATLAB:

Step 1. Set each entry of the matrix to an i.i.d. N(0,1) value.

Step 2. Orthogonalize the M rows of the matrix using the Gram-Schmidt algorithm.

Step 3. Normalize the rows of the matrix to unit length.

I do not know how to implement second step of above.

Any help is appreciated.

Answer 1

You might want to look at orth:

A = randn( m, n );  % random iid ~N(0,1)
oA = orth( A.' ).'; % orthogonal rows
nA = bsxfun( @rdivide, oA, sqrt( sum( oA.^2, 2 ) ) ); % normalize to unit length