Let A CX. Show that there exists a unitary matrix Q such that A =...
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Let A € C"X". Show that there exists a unitary matrix Q such that A = QAQ. Problem 8 Let A € CMX" has rank n. Show that there is a factorization of A = PH, where PE CX has orthonormal columns, and He C**" is Hermitian positive definite. If A € C" *", then, show that, JA- Pl2 S||A - Ql2 for any unitary matrix Q. Problem 9 Let A E CXN has rank n have a factorization A PH as in Problem 8. Show that |A' A - I12 <JA- Pla S 1+ ||A||2 |A*A - 1||2 Problem 10 Let A € Caxn and a >0. Show that o is a singular values of A if and only if the matrix 1. A -ol A* is singular. Let A € C"X". Show that there exists a unitary matrix Q such that A = QAQ. Problem 8 Let A € CMX" has rank n. Show that there is a factorization of A = PH, where PE CX has orthonormal columns, and He C**" is Hermitian positive definite. If A € C" *", then, show that, JA- Pl2 S||A - Ql2 for any unitary matrix Q. Problem 9 Let A E CXN has rank n have a factorization A PH as in Problem 8. Show that |A' A - I12 <JA- Pla S 1+ ||A||2 |A*A - 1||2 Problem 10 Let A € Caxn and a >0. Show that o is a singular values of A if and only if the matrix 1. A -ol A* is singular.
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Related Book For
Introduction to Real Analysis
ISBN: 978-0471433316
4th edition
Authors: Robert G. Bartle, Donald R. Sherbert
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