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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 12

12Bilinear and quadratic forms

Bilinear forms and congruence, quadratic forms, positive definiteness and min–max, and forms over arbitrary fields.

In this chapter

12.1Bilinear forms Beyond 21-242
12.2Quadratic forms
12.3Positive definiteness and min–max
12.4Inner products beyond ℝ and ℂ Beyond 21-242
12.5Proof patterns

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