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1Vector spaces
2Linear maps and matrices
3Linear systems and row reduction
4Dimension
5Determinants
6Inner product spaces
7Eigenvalues and diagonalization
8The spectral theorems
9The singular value decomposition
10Generalized eigenspaces and Jordan form
11Markov chains and positive matrices
12Bilinear and quadratic forms
13Duality and multilinear algebra*
14Linear algebra and abstract algebra*
15Infinite-dimensional vector spaces*
16Applications to data and machine learning*
ASets, functions, and proofs
BComplex numbers
1. Overview
2. B.1Complex numbers
CThe Fundamental Theorem of Algebra*
1. Overview
2. C.1Proofs of the Fundamental Theorem of Algebra

Index of techniques
Practice
PDF

Chapter 6

6Inner product spaces

Inner products and norms, Cauchy–Schwarz, orthonormal bases, projections, least squares, and adjoints.

In this chapter

6.1Inner products and norms
6.2Cauchy–Schwarz and the triangle inequality
6.3Orthogonality and orthonormal bases
6.4Orthogonal projection and Gram–Schmidt
6.5Least squares
6.6Adjoints
6.7Proof patterns

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