Prove as follows the inequality |Ax| =||A|| - |x|, where A is an m x m matrix with row vectors a1, a2, ..., am, and x is an m-dimensional vector. First note that the components of the vector Ax are aj · X, a2 • X, . .. , am • X, so 1/2 |Ax| = Σα2 Σ(a - x2 Then use the Cauchy-Schwarz inequality (a - x)? Ja2|x|? for the dot product. VI

Prove as follows the inequality |Ax| =||A|| - |x|, where A is an m x m matrix with row vectors a1, a2, ..., am, and x is an m-dimensional vector. First note that the components of the vector Ax are aj · X, a2 • X, . .. , am • X, so 1/2 |Ax| = Σα2 Σ(a - x2 Then use the Cauchy-Schwarz inequality (a - x)? Ja2|x|? for the dot product. VI

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.2: Norms And Distance Functions

Problem 33EQ

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