November 27th, 2016, 02:43 PM  #1 
Newbie Joined: Nov 2016 From: Pasay Posts: 1 Thanks: 0  Matrix property?
Let A be an m x n matrix. Show that the matrix $A^{T}A$ has the property that $x^{T}(A^{T}A)≥ 0$ for every $x ∈ R^{n}$. How do I start to prove this? I tried doing this: $x^{T}(A^{T}A) ≥ 0$ $(Ax)^{T}A ≥ 0$ But, I got stuck because this doesn't show $A^{T}A$ to be positive. Help is greatly appreciated, thank you. 

Tags 
matrix, property 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Matrix property  Tutu  Linear Algebra  1  January 18th, 2013 09:01 PM 
On one property of matrix  golomorf  Linear Algebra  2  December 26th, 2012 09:35 AM 
Matrix Property  tiba  Linear Algebra  3  June 18th, 2012 01:31 PM 
A property of a^b + b^a  elim  Real Analysis  1  November 25th, 2010 01:39 PM 
Matrix Property  tiba  Algebra  3  January 1st, 1970 12:00 AM 