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.

I was making matrix exercises when I ran into the matrix notation $X^{-2}$

Where $X$ is a $n \times n$ matrix. What is a matrix to the power $-2$?

Please provide me an answer because I couldn't find it anywhere else on the web.

share|improve this question
    
Could it be a typo? –  Student Feb 16 '13 at 13:54
    
No I already found it the answer. Thanks. It's the product of two inverser so X^(-1)X(-1) –  Sjoerd Smaal Feb 16 '13 at 13:56
add comment

1 Answer

In general for an $nxn$ matrix $A$, $A^k = A*A *...*A$ with the right hand side being multiplied $k$ times (which is well defined because of the associativity of matrixes).

In your case $A^{-2} = {(A^{-1})}^2 = A^{-1}*A^{-1}$, of course provided $A^{-1}$ exists.

share|improve this answer
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.