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January 10th, 2016, 03:20 PM   #1
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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
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January 10th, 2016, 05:34 PM   #2
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$\begin{pmatrix}
1/3 & -2/3 & -2/3\\
-2/3 & 1/3 & -2/3\\
-2/3 & -2/3 & 1/3
\end{pmatrix}$ is a possibility.
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January 11th, 2016, 04:06 AM   #3
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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
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January 11th, 2016, 07:47 AM   #4
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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
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January 11th, 2016, 09:25 AM   #5
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$\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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