Kunze Linear Algebra · Problem 6.4.10

Elementary Canonical Forms

Mathematics — Methods · real-3x3-not-triangulable-implies-diagonalizable-complex

Problem

Let

A

be a

3 \times 3

matrix with real entries. Prove that, if

A

is not similar over

R

to a triangular matrix, then

A

is similar over

C

to a diagonal matrix.