16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 9.2.3

Operators on Inner Product Spaces

Mathematics — Linear Algebra · forms-inner-product

Problem

Let

A = \begin{bmatrix} 1 & i \\ -i & 2 \end{bmatrix}

and let

g

be the form (on the space of

2 \times 1

complex matrices) defined by

g(X, Y) = Y^* A X

. Is

g

an inner product?