Orthogonality

Arindama Singh ()
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Arindama Singh: Indian Institute of Technology Madras, Department of Mathematics

Chapter Chapter 4 in Introduction to Matrix Theory, 2021, pp 81-99 from Springer

Abstract: Abstract Orthogonality is central to manipulating vectors in the plane and the three dimensional space. This notion is extended to the n dimensional space by an inner product, which is a simple generalization of the dot product of plane vectors. With the help of orthogonality and orthonormality it is shown that the Gram–Schmidt process yields an orthogonal and/or an orthonormal basis for a subspace. This leads to the QR-factorization of a matrix. Using the notion of orthogonal projections, a best approximation of a vector from a subspace and the least square solution of a system of linear equations are obtained.

Date: 2021
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DOI: 10.1007/978-3-030-80481-7_4

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