January 10th, 2016, 03:20 PM  #1 
Senior Member Joined: Nov 2013 Posts: 137 Thanks: 1  3x3 Matrix
Hi! I have a doubt... Look this matrix equation: By analogy, should exist a matrix 3x3 such that: So, what values need be replaced in ? for the matrix equation above be right? Thanks, Henry 
January 10th, 2016, 05:34 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,916 Thanks: 2199 
$\begin{pmatrix} 1/3 & 2/3 & 2/3\\ 2/3 & 1/3 & 2/3\\ 2/3 & 2/3 & 1/3 \end{pmatrix}$ is a possibility. 
January 11th, 2016, 04:06 AM  #3 
Senior Member Joined: Nov 2013 Posts: 137 Thanks: 1 
But, this is not the answer that I'm looking for... Would be the answer in this below pages? https://en.wikipedia.org/wiki/Quadra...nge_resolvents https://en.wikipedia.org/wiki/Cubic_...nge.27s_method https://en.wikipedia.org/wiki/Quarti...ange_resolvent 
January 11th, 2016, 07:47 AM  #4 
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 
The OP question is: What is the square root of a 3x3 identity matrix? Given X, find M st A=MX and X=MA > M^2=I OP gives M for 2x2 I, M^2=I checks 
January 11th, 2016, 09:25 AM  #5 
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 
$\displaystyle M=\begin{vmatrix} 1/\sqrt{2} &1/\sqrt{2} &0 \\ 1/\sqrt{2} & 1/\sqrt{2} &0 \\ 0& 0 & 1 \end{vmatrix}\\ $ by inspection. ref previous post. This is a square root, not the square root. Last edited by zylo; January 11th, 2016 at 09:29 AM. 

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