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Orthogonality

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Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

Orthogonality is the mathematical formalization of the geometrical property of perpendicularity, as adapted to general inner product spaces. In linear algebra, bases consisting of mutually orthogonal elements play an essential role in theoretical developments, in a broad range of applications, and in the design of practical numerical algorithms. Computations become dramatically simpler and less prone to numerical instabilities when performed in orthogonal coordinate systems. Indeed, many large-scale modern applications would be impractical, if not completely infeasible, were it not for the dramatic simplifying power of orthogonality.

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  • DOI: 10.1007/978-3-319-91041-3_4
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Olver, P.J., Shakiban, C. (2018). Orthogonality. In: Applied Linear Algebra. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-91041-3_4

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