December 15th, 2016, 12:19 AM  #1 
Newbie Joined: Dec 2016 From: Haifa Posts: 1 Thanks: 0  Matrix and vectors
1. In given A in size of mXn while m>n and: (A^T)*A=I. What can i say about the eigenvalues of A*(A^T)? and why? 
December 15th, 2016, 06:24 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,970 Thanks: 2291 Math Focus: Mainly analysis and algebra 
Try writing out an explicit example.

December 20th, 2016, 12:42 PM  #3 
Member Joined: Dec 2016 From:  Posts: 54 Thanks: 10 
If your matrix is m x n dimensional, unless m=n I dont see how do you want to get the eigenvalues.... They are only possible to calculate in square matrices

December 20th, 2016, 01:41 PM  #4 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,490 Thanks: 749  
December 20th, 2016, 01:53 PM  #5 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,490 Thanks: 749  you're given $A^T A=I$ you want the eigenvalues of $A A^T$ $A A^T x = \lambda x$ $A^T A A^T x = A^T \lambda x = \lambda A^T x$ $I A^T x = A^T x = \lambda A^T x$ what does this say about $\lambda$ and/or $A^T x$ ? 
December 20th, 2016, 02:14 PM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,970 Thanks: 2291 Math Focus: Mainly analysis and algebra 
I would just form $A^TA=I \implies AA^TA=AI=A$ so the columns of $A$ are eigenvectors of $(AA^T)$ with eigenvalues of...

December 20th, 2016, 02:47 PM  #7 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,490 Thanks: 749  

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