Conversation started Jan 6, 2017 at 3:48.
heather
heather
Jan 6, 2017 03:48
specifically, how do you take the square root of a matrix?
Martin Sleziak
Martin Sleziak
@heather Do you have a specific matrix? Or is it for arbitrary matrix? What are the dimensions? Are eigenvalues positive?
heather
heather
@MartinSleziak, well, it was for the matrix $\begin{bmatrix}0&1\\1&0\end{bmatrix}$
Martin Sleziak
Martin Sleziak
Wikipedia article might be helpful: Square root of a matrix
heather
heather
ah, okay, thank you
that should help
Martin Sleziak
Martin Sleziak
Oh, this is basically taking the square root of $i$ in $\mathbb C$.
heather
heather
Jan 6, 2017 03:53
okay
I've never even realized you could do $\sqrt{i}$
i guess i've never thought of it.
the fourth root of -1
Martin Sleziak
Martin Sleziak
If you wish, you can also have a look at my answer here: Finding complex solution to $X^2 = A$
heather
heather
okay
thank you.
Martin Sleziak
Martin Sleziak
Another way to look at this problem - it is rotation with angle $\pi/2$.
And you want a linear map $f$ such that $f\circ f=R_{\pi/2}$.
The fact that this is a rather simple matrix makes things easier.
But in general for $2\times2$ matrices this should not be too difficult.
And of course, diagonalization should work here too.
 
Conversation ended Jan 6, 2017 at 4:00.