Tagging - 2016-05-07

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5:48 AM

There are probably many questions related to square root of a matrix.

Standard tag for square root is radicals. (The tag roots has a different meaning.)

First I thought that it might be good idea to use the tag (radicals) for such questions. But I see that this not agree with the tag-excerpt: "For questions involving radical numbers or expressions (i.e. expressions which involve $\sqrt[n]{\text{something}}$)."

What do you think about this usage of (radicals). Should we expand the tag-excerpt.

So far I have ratagged only 3 questions. So it will not be much work to revert the changes, if we decide to doso.

Q: Computing $ \mathbf A^{-1/2}$, where $ \mathbf A$ is a Diagonal Matrix.

I have the following matrix : $$ \mathbf A =\begin{bmatrix} 100 & 0 \\ 0 & 1 \\ \end{bmatrix}$$ I have to compute $ \mathbf A^{-1/2}$. So I need spectral decomposition, $$ \mathbf A = \mathbf P \mathbf \Lambda\mathbf P',$$ $\mathbf P$ be a matrix with normalized eigenvec...

Q: For every matrix $A\in M_{2}( \mathbb{C}) $ there's $X\in M_{2}( \mathbb{C})$ such that $X^2=A$?

True\False? For every matrix $A\in M_{2}( \mathbb{C}) $ there's $X\in M_{2}( \mathbb{C})$ such that $X^2=A$. I know that every complexed matrix has a Jordan form matrix $J$ such that $P^{-1}CP=J$, But it's not diagonalizable for sure. Thanks

linear-algebra matrices matrix-equations radicals

Q: $A = B^2$ for which matrix $A$?

Is it true that for any $A\in M(n,\mathbb{C})$there exist a $B\in M(n,\mathbb{C})$ such that $A = B^2$? I think this is not true (but I don't know nay example), and then is it possible to characterize such $A$?