Inner Product Spaces

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

Chapter 15 in The Linear Algebra a Beginning Graduate Student Ought to Know, 2012, pp 333-367 from Springer

Abstract: Abstract Real and complex inner product spaces are defined and several examples are studied. Elementary properties of inner products, such as the Cauchy–Schwarz–Bunyakovsky Theorem and Minkowski’s inequality are proven. The Lagrange identity relating inner and cross products in three-dimensional real vector spaces is proven. Normed spaces are defined and various examples of norms are considered, including spectral norms and various matrix norms. The Hahn–Banach Theorem, Gershgorin’s Theorem, and the Diagonal Dominance Theorem are proven. Matrix exponentials are studied.

Keywords: Product Space; Gershgorin; Matrix Exponential; Spectral Norm; Real Euclidean (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_15

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DOI: 10.1007/978-94-007-2636-9_15

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