Square Root of Matrix
I have been experimenting with matrices lately and I am
wondering whether it is possible to take the square-root of a square
matrix (square matrices primarily because of course it is not possible
with un even matrices such as a 3 x 2 matrix since multiplication is not
commutative in matrix mathematics). I know for a fact that it is possible
with 2 x 2 matrices (I have done it myself), but how about for larger
square matrices such as 3 x 3 or 4 x 4?
Apparently there is no universal algorithm for |M|^1/2. Since you are
experimenting with matrix operations, I assume you are not intimidated by
matrix operations and notation. The two sites below discuss the problem of
finding the square root for some special cases. If you do a google search
on the term "matrix square root" you will find numerous sites and
discussions of the problem.
I encourage you to continue your interest in mathematics. It will serve
you well no matter what field of endeavor you undertake.
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Update: June 2012