Since m is upper triangular and normal we know that

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: pper triangular, which implies that M is normal. Since M is − upper triangular and normal, we know that it is diagonal. Since the eigenvalues of R2 R1 1 are − strictly positive and have magnitude 1, we know that R2 R1 1 = I = Q∗ Q1 . Thus, R2 = R1 and 2 Q2 = Q1 . Hence, the factorization is unique. \\ 1 Existence: Use Gram Schmidt. We assume A is invertible, so its column vectors are linearly independent. We can form an orthonormal basis. Let A = [a1 a2 · · · an ]. We form the orthonormal ba...
View Full Document

This note was uploaded on 01/16/2014 for the course MATH 6304 taught by Professor Bernhardbodmann during the Fall '12 term at University of Houston.

Ask a homework question - tutors are online