Linear Algebra Done Right · Problem 5D.11

Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · diagonalizable-operators

Problem

Find

T \in \mathcal{L}(\mathbf{C}^3)

such that

6

and

7

are eigenvalues of

T

and such that

T

does not have a diagonal matrix with respect to any basis of

\mathbf{C}^3