Linear Algebra Done Right · Problem 7C.3

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · positive-operators

Problem

Suppose

n

is a positive integer and

T \in \mathcal{L}(\mathbf{F}^n)

is the operator whose matrix (with respect to the standard basis) consists of all 1's. Show that

T

is a positive operator.