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There is any generic mathematical expression (formula) to represent a Matrix squared ?

I search it before, but i didn't find.


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closed as too localized by Jacques Carette, Bill Johnson, Qiaochu Yuan, Will Jagy, Suvrit Nov 18 '11 at 20:46

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This is not research level - try And the answer is no, there isn't beyond A^2. – Jacques Carette Nov 18 '11 at 20:14
$A$ squared = $A.A$ – Anthony Quas Nov 19 '11 at 2:06
up vote 1 down vote accepted

If your question is to be interpreted as asking for the image of the squaring map for square matrices of a given size n over a given field: then the only superficially obvious condition is that the determinant should be a square. Over the complex number field "almost all" square matrices are squares; but it is not true in general that all matrices are squares. That is something you can read off from the Jordan normal form.

I suppose that one can use abstract algebraic geometry to claim that the matrices that are squares are a constructible set. This gives one some idea that there is reasonable answer for a given n. But it may not be very useful.

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That's a very imaginative interpretation of what the question might have been! :) – Mariano Suárez-Alvarez Nov 19 '11 at 0:21

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