Inner Product Spaces
A 20-module path through inner product spaces, in study order from foundations to the frontier.
Modules
- Inner Products and Inner Product Spaces
- Norms Induced by Inner Products
- The Cauchy-Schwarz Inequality
- The Triangle Inequality and Norm Properties
- Orthogonality and Orthogonal Sets
- Orthonormal Bases and Coordinates
- The Gram-Schmidt Process
- Existence of Orthonormal Bases
- Bessel and Parseval Identities
- Orthogonal Complements
- Orthogonal Projections
- The Minimum Distance Property
- The Adjoint of a Linear Map
- Self-Adjoint Operators
- Normal Operators
- The Complex Spectral Theorem
- The Spectral Theorem for Self-Adjoint Operators
- Positive Operators and Square Roots
- The Singular Value Decomposition
- The Polar Decomposition