I was wondering about the following: $m>1$ integer, and $A$ real matrix. $A^m=0$. Is $t=0$ the only eigenvalue of A?
Is it true?
I was wondering about the following: $m>1$ integer, and $A$ real matrix. $A^m=0$. Is $t=0$ the only eigenvalue of A?
Is it true?
Recall the definition of an eigenvalue. $\lambda $ is an eigenvalue of $A$ if there exists a vector $v$ such that $Av=\lambda v$. Hence $A^m v=\lambda^m v$. But what is $A^m v$ if $A^m$ is the all zeros matrix? What does that tell us about the other side $\lambda^m v$? Can you solve it from here?