Given an M x N matrix, is there a way to produce an orthogonal set of N vectors of length M, where M < N?

Question

Gram-Schmidt orthogonalization would only use the first M vectors to generate a basis of size M x M.

My question is: given an M x N matrix, is there a way to produce an orthogonal set of N vectors of length M, where M < N — Jack, Jun 23 '13 at 02:58

score 0 · Answer 1 · answered Jun 23 '13 at 03:10

0

Hint: A set of orthogonal vectors is linearly independent. Think about a basis for the space.

answered Jun 23 '13 at 03:10

Ross Millikan

For this statement to be correct, you need to insert nonzero. – Ted Shifrin Jun 23 '13 at 04:01

1 Answers1