User Name Remember Me? Password

 Abstract Algebra Abstract Algebra Math Forum

April 6th, 2016, 09:24 AM   #1
Newbie

Joined: Jun 2015
From: Warsaw

Posts: 3
Thanks: 1

Proof concerning matrix norm.

Hi, I am struggling with following proof, could you give me some hint or some information which would help me in proving following inequality?
Attached Images proof2.png (6.0 KB, 11 views) June 1st, 2016, 07:25 AM #2 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 Definition* ||A||$\displaystyle _{\infty}$=max sum of absolute values of row elements. Theorem ||AB||$\displaystyle _{\infty} \leq$ ||A||$\displaystyle _{\infty}$||B||$\displaystyle _{\infty}$ Proof Consider A & B 2x2 and elements are the absolute values: Sum each row of AB: 1st row sum= a11(b11+b12) + a12(b21+b22) 2nd row sum= a21(b11+b12) + a22(b21+b22) Assume (b11+b12)$\displaystyle \leq$(b21+b22) 1st row sum$\displaystyle \leq$ (a11+a12)(b21+b22) 2nd row sum$\displaystyle \leq$ (a21+a22)(b21+b22) Assume (a11+a12)$\displaystyle \leq$(a21+a22) 1st row sum$\displaystyle \leq$ (a21+a22)(b21+b22) 2nd row sum$\displaystyle \leq$ (a21+a22)(b21+b22) In general, max of sum of absolute values of elements of rows of AB $\displaystyle \leq$ (max of sum of absolute values of elements of rows of A)( max of sum of absolute values of elements of rows of B). ||AB||$\displaystyle _{\infty} \leq$ ||A||$\displaystyle _{\infty}$||B||$\displaystyle _{\infty}$ * https://en.wikipedia.org/wiki/Matrix_norm Thanks from manus Last edited by zylo; June 1st, 2016 at 07:32 AM. Tags matrix, norm, proof Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post hegendroffer Abstract Algebra 2 June 2nd, 2016 04:30 AM mnnejati Calculus 0 April 6th, 2015 11:04 AM Student444 Linear Algebra 4 February 5th, 2012 10:30 PM onako Linear Algebra 0 February 1st, 2012 12:59 AM ricconna Linear Algebra 0 August 23rd, 2011 08:55 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top

Copyright © 2019 My Math Forum. All rights reserved.      