MP1 · Linear algebra & function spaces
A 21-module path through mp1 · linear algebra & function spaces, in study order from foundations to the frontier.
Modules
- Vector Spaces and Subspaces
- Linear Independence, Basis, and Dimension
- Linear Operators and Matrix Representations
- Change of Basis and Similarity Transformations
- Rank, Nullity, and the Fundamental Theorem of Linear Maps
- Determinants and Their Properties
- Eigenvalues, Eigenvectors, and the Characteristic Equation
- Diagonalization and the Spectral Decomposition
- Jordan Canonical Form and Defective Matrices
- Inner-Product Spaces and Norms
- Orthogonality and the Gram-Schmidt Process
- Adjoint Operators and Hermitian Operators
- Unitary and Orthogonal Operators
- Normal Operators and the Spectral Theorem
- Bilinear and Quadratic Forms
- Dual Spaces and Linear Functionals
- Tensor Products of Vector Spaces
- Infinite-Dimensional Function Spaces
- Completeness, Cauchy Sequences, and Banach Spaces
- Hilbert Spaces and Orthonormal Bases
- Bounded and Unbounded Operators on Hilbert Space