Kunze Linear Algebra · Problem 8.2.13

Inner Product Spaces

Mathematics — Methods · orthogonal-complement

Problem

Let

S

be a subset of an inner product space

V

. Show that

(S^\perp)^\perp

contains the subspace spanned by

S

. When

V

is finite-dimensional, show that

(S^\perp)^\perp

is the subspace spanned by

S