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.
Let $A$ be a square matrix such that $A^2 = A$. Show that $A$ cannot be a strictly diagonally dominated matrix unless A is the identity matrix.
0
$\begingroup$
matrices
-
0Well, what do you $k$now about "strictly diagonally dominated" matrices? Any theorems? – 2012-03-04
1 Answers
2
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 $A$.