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.

Let $A$ be a square matrix such that $A^2 = A$. Any idea how to show that $A$ cannot be a strictly diagonally dominated matrix unless $A$ is the identity matrix.

share|improve this question
    
Well, what do you know about "strictly diagonally dominated" matrices? Any theorems? –  Gerry Myerson Mar 4 '12 at 22:56
6  
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are so far; this will prevent people from telling you things you already know, and ensure that they write their answers at an appropriate level. If this is homework, please add the [homework] tag; people will still help, so don't worry. Also, many find the use of imperative ("Prove", "Show") to be rude when asking for help; please consider rewriting your post. –  Arturo Magidin Mar 4 '12 at 22:59
add comment

1 Answer

Write the equality as $A(A-I)=0$ and use the fact that strictly diagonally dominated matrices are invertible (you can prove that, right?) to eliminate $A$.

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.