More specifically, how do you define the square root of an $n\times n$ matrix A and express it in linear algebra terms? Does this have something to do with positive semi-definite matrices and diagonalization?
How do you define the square root of a matrix?
1
$\begingroup$
matrices
-
0Related posts: http://math.stackexchange.com/questions/57292/for-every-matrix-a-in-m-2-mathbbc-theres-x-in-m-2-mathbbc-s, http://math.stackexchange.com/questions/65227/square-root-of-a-matrix, http://math.stackexchange.com/questions/72551/a-question-about-n-times-n-matrix – 2011-12-21
1 Answers
3
Square root of a matrix $A$ is another matrix $B$ such that $B^2 = A$. It might or might not exist and it might or might not be unique. See Wikipedia for more.
-
4"might or might not be unique": It is *never* unique unless $n=1$ and $A=0$, or unless you impose additional conditions such as positivity. (If A is positive semidefinite, then it has a unique positive semidefinite square root.) – 2011-12-21