Linear Algebra Done Right · Problem 6C.3

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · orthogonal-complements

Problem

Suppose

U

is the subspace of

\mathbf{R}^4

defined by

U = \operatorname{span}((1, 2, 3, -4), (-5, 4, 3, 2)).

Find an orthonormal basis of

U

and an orthonormal basis of

U^\perp