There are some conditions under which there are unique square-roots for
some matrices, but not others.
For example, a : matrix([0.8,0.5],[0.2,0.5]);
Unique square-root:
matrix([0.87077787570164,0.3230553107459],[0.12922212727859,0.67694468180352])
But consider matrix matrix([33,24],[48,57]); This has *two* square
roots: matrix(91,4],8,5]) and matrix([5,2],[4,7]);
But, your point concerning no standard definition 'in general' seems
to be correct. There has been a fair bit of work on the problem - some
of which I can actually follow! ;-)
On 12/28/2012 10:50 AM, Stavros Macrakis wrote:
> The ^^ operator doesn't do anything with fractional powers. One
> reason for that is that they are not unique. For example, there are
> infinitely many solutions
> <http://en.wikipedia.org/wiki/Square_root_of_a_matrix>; to
> a^^2=ident(2); one infinite family is matrix([1,0],[%r1,-1]) for
> arbitrary %r1. I don't believe there is any standard definition of a
> "principal value" of the matrix square root in general.
>
> -s
>
>
> On Fri, Dec 28, 2012 at 10:30 AM, Evan Cooch <evan.cooch at gmail.com
> <mailto:evan.cooch at gmail.com>> wrote:
>
>
> "? matrix" is your friend. It's not clear exactly what you did,
> but the
> documentation there says that A^2 squares the elements of a
> matrix, but
> A^^2 is the matrix product of A and A, which is probably what you
> wanted.
>
> Ray
>
> Thank you. A^^2 is indeed what I wanted.
>
>
>
>
> That approach seems to work fine, so long as you are interested in
> integer powers of a matrix (which seems to be the case here). The
> approach I posted earlier is more general. Suppose, for example,
> you want the square-root of A? A^^(0.5) doesn't evaluate.
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