16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 6.2.12

Elementary Canonical Forms

Mathematics — Linear Algebra · 2x2-complex-matrix-canonical-form

Problem

Use the result of Exercise 11 to prove the following: If

A

is a

2 \times 2

matrix with complex entries, then

A

is similar over

C

to a matrix of one of the two types

\begin{bmatrix} a & 0 \\ 0 & b \end{bmatrix} \qquad \begin{bmatrix} a & 0 \\ 1 & a \end{bmatrix}.