16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 6.2.15

Elementary Canonical Forms

Mathematics — Linear Algebra · left-multiplication-characteristic-values

Problem

Let

V

be the space of

n \times n

matrices over

F

. Let

A

be a fixed

n \times n

matrix over

F

. Let

T

be the linear operator 'left multiplication by

A

' on

V

. Is it true that

A

and

T

have the same characteristic values?