Linear Algebra Done Right · Problem 5E.1

Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · commuting-operators

Problem

Give an example of two commuting operators

S, T

\mathbf{F}^4

such that there is a subspace of

\mathbf{F}^4

that is invariant under

S

but not under

T

and there is a subspace of

\mathbf{F}^4

that is invariant under

T

but not under

S