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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...
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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.
 Fall '12
 BernhardBodmann
 Math, Matrices

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