5. (10pts) Let A be a positive definite nxn matrix. For any x = R", let ||X||A = √(Ax, x). Show that this defines a vector norm on Rn.
5. (10pts) Let A be a positive definite nxn matrix. For any x = R", let ||X||A = √(Ax, x). Show that this defines a vector norm on Rn.
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
Question
![5. (10pts) Let A be a positive definite nxn matrix. For any x = R", let
||X||A = √(Ax, x). Show that this defines a vector norm on Rn.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6389447-1237-4af0-b5c6-eb1260425b55%2F8b530c79-93ab-45ad-840c-b661c0729835%2Fmds0k2_processed.png&w=3840&q=75)
Transcribed Image Text:5. (10pts) Let A be a positive definite nxn matrix. For any x = R", let
||X||A = √(Ax, x). Show that this defines a vector norm on Rn.
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