TITLE:
Projections and Reflections in Vector Space
AUTHORS:
Kung-Kuen Tse
KEYWORDS:
Projection, Reflection, Commute, Inner Product, Affine Subspace
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.6 No.6,
May
19,
2016
ABSTRACT: We study projections onto a subspace and reflections with respect to a
subspace in an arbitrary vector space with an inner product. We give necessary
and sufficient conditions for two such transformations to commute. We then
generalize the result to affine subspaces and transformations.