Orthogonality

Jonathan S. Golan ()
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Jonathan S. Golan: University of Haifa, Dept. of Mathematics

Chapter 16 in The Linear Algebra a Beginning Graduate Student Ought to Know, 2012, pp 369-394 from Springer

Abstract: Abstract The notion of orthogonality in an inner product space is introduced and several examples are presented, including Legendre and Chebyshev polynomials. The Gram–Schmidt Theorem and Hadamard’s inequality are proven. Orthogonal complements of subspaces are introduced, as are orthogonal projections. Every finitely-generated inner product space is shown to have an orthonormal basis and the properties of orthonormal bases are studied. QR-decompositions are introduced. The Riesz Representation Theorem is proven for finitely-generated inner product spaces. The notion of the adjoint of a linear transformation between inner product spaces is introduced and studied.

Keywords: Product Space; Subspace; Hilbert Subset; Pafnuty Lvovich Chebyshev; Lagrange Identity (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-007-2636-9_16

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DOI: 10.1007/978-94-007-2636-9_16

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