16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 4.2.3

Polynomials

Mathematics — Linear Algebra · polynomial-evaluation-diagonal-matrix

Problem

Let

A

be an

n \times n

diagonal matrix over the field

F

, i.e., a matrix satisfying

A_{ij} = 0

for

i \neq j

. Let

f

be the polynomial over

F

defined by

f = (x - A_{11}) \cdots (x - A_{nn}).

What is the matrix

f(A)