Let be a polynomial of degree n in x with real coefficients. For any mxm matrix A, we define .
Show that, if and , then A must be invertible. [Hint: isolate Im from the equation P(A) = 0m]
Let be a polynomial of degree n in x with real coefficients. For any mxm matrix A, we define .
Show that, if and , then A must be invertible. [Hint: isolate Im from the equation P(A) = 0m]