Linear Algebra Done Right · Problem 5D.10

Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · diagonalizable-operators

Problem

Find

R, T \in \mathcal{L}(\mathbf{F}^4)

such that

R

and

T

each have

2, 6, 7

as eigenvalues,

R

and

T

have no other eigenvalues, and there does not exist an invertible operator

S \in \mathcal{L}(\mathbf{F}^4)

such that

R = S^{-1}TS