Transcription of Inner Product, Orthogonality, and Orthogonal Projection
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Inner Product, Orthogonality, and Orthogonal Projection
Math 240TA: Shuyi WengWinter 2017 March 2, 2017 Inner Product, Orthogonality, and Orthogonal ProjectionInner ProductThe notion ofinner productis important in linear algebra in the sense that it providesa sensible notion of length and angle in a vector space. This seems very natural in theEuclidean spaceRnthrough the concept ofdot product. However, the Inner product ismuch more general and can be extended to other non-Euclidean vector spaces. For thiscourse, you are not required to understand the non-Euclidean examples. I just want toshow you a glimpse of linear algebra in a more general setting in a vector space. Aninner productonVis a function , :V V Rsuch that for all vectorsu, v, w Vand scalarc R, it satisfies the axioms1.
Math 240 TA: Shuyi Weng Winter 2017 March 2, 2017 Inner Product, Orthogonality, and Orthogonal Projection Inner Product The notion of inner product is important in linear algebra in the sense that it provides a sensible notion of length and angle in a vector space.
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