Projections and Reflections in Vector Space - Advances in Pure Mathematics

APM > Vol.6 No.6, May 2016

Advances in Pure Mathematics

Volume 6, Issue 6 (May 2016)

ISSN Print: 2160-0368 ISSN Online: 2160-0384

Google-based Impact Factor: 0.50 Citations h5-index & Ranking

Projections and Reflections in Vector Space ()

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DOI: 10.4236/apm.2016.66030 4,154 Downloads 4,991 Views Citations

Author(s)

Kung-Kuen Tse

Affiliation(s)

Department of Mathematics, Kean University, Union, NJ, USA.

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.

KEYWORDS

Projection, Reflection, Commute, Inner Product, Affine Subspace

Share and Cite:

Tse, K. (2016) Projections and Reflections in Vector Space. Advances in Pure Mathematics, 6, 436-440. doi: 10.4236/apm.2016.66030.

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