Kunze Linear Algebra · Problem 8.3.2

Inner Product Spaces

Mathematics — Methods · adjoints-linear-operators

Problem

Let

T

be the linear operator on

C^2

defined by

T\epsilon_1 = (1 + i, 2)

T\epsilon_2 = (i, i)

. Using the standard inner product, find the matrix of

T^*

in the standard ordered basis. Does

T

commute with

T^*