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Inner Product Spaces

In: The Linear Algebra a Beginning Graduate Student Ought to Know

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  • Jonathan S. Golan

    (University of Haifa, Dept. of Mathematics)

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.

Suggested Citation

  • Jonathan S. Golan, 2012. "Inner Product Spaces," Springer Books, in: The Linear Algebra a Beginning Graduate Student Ought to Know, edition 3, chapter 15, pages 333-367, Springer.
    • Handle: RePEc:spr:sprchp:978-94-007-2636-9_15
    DOI: 10.1007/978-94-007-2636-9_15
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