If is zero, then . But since is invertible...
Here is my problem:
Let A be a complex n x n matrix with minimal polynomial q(x)=the sum from j=0 to m of where and = 1.
Show: If A is non-singular then does not equal 0.
So, I get that 0=q(A)= , but I'm not sure what to do here. I assume we will have to use the fact that A is non-singular, but I'm not sure how. Does it maybe involve multiplying both sides by x on the right side? Any hints would be much appreciated!
I have tried before to assume that is 0, but I can't figure out what to do after. Because A is invertible, we can multiply both sides by so we get:
0= .
Buth I haven't been able to understand how that poses a contradiction.
Does it imply that all the alphas would have to be 0? Which would be aproblem because was given to be equal to 1.