Linear Algebra and Its Applications · Problem 3.1.36

Orthogonality — Gilbert Strang

Mathematics · orthogonal-subspaces

Problem

Extend Problem 35 to a

p

-dimensional subspace

V

and a

q

-dimensional subspace

W

\mathbf{R}^n

. What inequality on

p+q

guarantees that

V

intersects

W

in a nonzero vector? These subspaces cannot be orthogonal.