Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question
3  
I think this wiki article should do the deal: en.wikipedia.org/wiki/Square_root_of_a_matrix –  user21436 Dec 21 '11 at 21:21
    
add comment

1 Answer 1

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.

share|improve this answer
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.) –  Jonas Meyer Dec 21 '11 at 21:29
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.