Parallel projection

The transformation P is the orthogonal projection onto the line m.

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that P² = P. Projections map the whole vector space to a subspace and leave the points in that subspace unchanged.

References

• N. Dunford and J.T. Schwartz, Linear Operators, Part I: General Theory, Interscience, 1958.
• Carl D. Meyer, Matrix Analysis and Applied Linear Algebra, Society for Industrial and Applied Mathematics, 2000. ISBN 978-0-89871-454-8.

Other websites

• MIT Linear Algebra Lecture on Projection Matrices at Google Video, from MIT OpenCourseWare