Linear Algebra II Spring 2026 Calendar
Week Date Topics Links
1 Monday
1/26/2026
  • Preliminaries
  • Abstract Linear Algebra
  • Abstract Matrix Notation
  • Linear Maps and Functions
 Slides
2 Monday
2/2/2026
  • Oriented Volume of Parallelopiped
  • Oriented Volume Functions
  • Permutations
  • Determinant of Linear Map
 Slides
3 Monday
2/9/2026
  • Eigenvalues and Eigenvectors
  • Characteristic Polynomial
  • Diagonal and Triangular Matrices
  • Diagonalizable Transformations
  • Eienspaces of Linear Map
 Slides
4 Tuesday
2/17/2026
  • Inner Product Spaces
  • Cauchy-Schwarz and Triangle Inequalities
  • Orthonormal Sets and Bases
 Slides
5 Monday
2/23/2026
  • Orthogonal Projection
  • Construction of Unitary Basis
  • Adjoint Maps and Matrices
  • Unitary Transformations and Matrices
 Slides
6 Monday
3/2/2026
  • Schur Decomposition
 Slides
7 Monday
3/9/2026
  • Self-Adjoint Transformations
  • Singular Value Decomposition
 Slides
Monday
3/16/2026		 No class Slides
8 Monday
3/23/2026
  • Quasisolutions to System of Linear Equations
  • Moore-Penrose Quasi-Inverse Operator
  • Unit Ball of Inner Product Space
  • Operator and Frobenius Norms of Linear Map
  • Condition Number of Linear Map
 Slides
9 Monday
3/30/2026		 Midterm
11 Monday
4/6/2026
  • Dual Vector Space
  • Tensors
  • Quadratic Forms
  • Complex Tensors
 Slides
12 Monday
4/13/2026
  • Hermitian Forms
  • Sylvester's Law of Inertia
  • Bilinear Form on Inner Product Space
  • Cayley-Hamilton Theorem
  • Spectral Gap Theorem
 Slides
13 Monday
4/20/2026
  • Isometries of Euclidean Space
 Slides
14 Monday
4/27/2026
  • Affine Geometry
 Slides
15 Monday
5/4/2026
  • Categories and Functors in Linear Algebra
 Slides
TBA Final Exam