Let A and B be m x n matrices and || || be any matrix norm for m x n matrices, prove that | || – 2||B|| + ||2B – || < 2|| A – B||.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.6: Matrices
Problem 21E: Suppose that A is an invertible matrix over and O is a zero matrix. Prove that if AX=O, then X=O.
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3. Let A and B be m x n matrices and || · || be any matrix norm for m x n matrices, prove
that
| | – 2||B|| + ||2B – A|| < 2||A – B||.
Transcribed Image Text:3. Let A and B be m x n matrices and || · || be any matrix norm for m x n matrices, prove that | | – 2||B|| + ||2B – A|| < 2||A – B||.
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