P1 Linear Algebra Lecture 2： Examples of vector spaces
P2 Linear Algebra Lecture 3： Subspaces and proofs of elementary properties
P3 Lecture 4： Sums and direct sums
P4 Lecture 5a direct sum criterion
P5 Lecture 5b： Linear combinations and span
P6 Lecture 6： Linear independence and dependence
P7 Lecture 7： Basis of a vector space, relationship to direct sum, dimension of
P8 Lecture 8： More on dimension, sum, and direct sum
P9 Lecture 9： Linear Transformations
P10 Lecture 10： Composition of linear transformations, composition, diagrams, ve
P11 Lecture 11： Linear maps- endomorphisms, nullspace, injective and surjective
P12 Lecture 12： More on range, null, injective, surjective, and rank-nullity
P13 Lecture 13： Matrices and linear transformations
P14 Lecture 14： Invertibility, inverse, isomorphism, and the case of operators
P15 Lecture 15： Operators, duals, dual basis
P18 Eigenvalues and Eigenvectors part 1
P19 Eigenvalues and eigenvectors part 2, normal forms
P20 Eigenvectors and eigenvalues 3, determinant and trace
P21 Trace and determinant as invariants, tensor product, diagrams
P22 Eigenvectors, eigenvalues, and invariant subspaces in real vector spaces
P23 Inner products part 1
P24 Inner Products part 2
P25 Inner Products part 3
P26 Inner products part 4： orthogonal complements and projection, optimization
P27 Linear functionals and adjoints part 1： Riesz representation, adjoint
P28 Linear functionals and adjoints part 2, self-adjoint maps
P29 Adjoints etc 3： properties, normal, complex spectral theorem
P30 Real Spectral Theorem
P31 Versions of spectral theorems; positive operators
