Does every element have a square root problem

DgrayMan · **Joined:** Sat, 21 Jan 2012 03:59:22 UTC **Posts:** 182

gotcha

Justin · **Joined:** Wed, 21 May 2003 04:27:18 UTC **Posts:** 996

Shadow wrote:

Justin wrote:

To original poster: Ignore my example, it doesn't work...although I do remember something from linear algebra about not every square matrix having a square root. I think that result is much harder than the problem intended.

Here is how complicated it can get with matrices: http://en.wikipedia.org/wiki/Square_root_of_a_matrix

Justin: if you want a matrix (over $\mathbb{R}$ say) without a square root, just get one with a negative determinant like $\begin{pmatrix} 1 & 0 \\ 0 & -1\end{pmatrix}$ .

Makes sense...so my original idea was not wrong then. Thanks!

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Does every element have a square root problem

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