MA-GY7043 Linear Algebra II Spring 2025 Calendar
Week Date Topics Links
1 Thursday
1/23/2025
  • Preliminaries
  • Abstract Linear Algebra
  • Abstract Matrix Notation
  • Linear Maps and Functions
 Slides
2 Thursday
1/30/2025
  • Oriented Volume of Parallelopiped
  • Oriented Volume Functions
  • Permutations
  • Determinant of Linear Map
 Slides
3 Thursday
2/6/2025
  • Eigenvalues and Eigenvectors
  • Characteristic Polynomial
  • Diagonal and Triangular Matrices
  • Diagonalizable Transformations
  • Eienspaces of Linear Map
 Slides
4 Thursday
2/13/2025
  • Inner Product Spaces
  • Cauchy-Schwarz and Triangle Inequalities
  • Orthonormal Sets and Bases
 Slides
5 Thursday
2/20/2025
  • Orthogonal Projection
  • Construction of Unitary Basis
  • Adjoint Maps and Matrices
  • Unitary Transformations and Matrices
 Slides
6 Thursday
2/27/2025
  • Schur Decomposition
 Slides
7 Thursday
3/6/2025
  • Self-Adjoint Transformations
  • Singular Value Decomposition
 Slides
8 Thursday
3/13/2025
  • 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 Thursday
3/20/2025		 Midterm
10 Thursday
3/27/2025		 No class
11 Thursday
4/3/2025
  • Dual Vector Space
  • Tensors
  • Quadratic Forms
  • Complex Tensors
 Slides
12 Thursday
4/10/2025
  • Hermitian Forms
  • Sylvester's Law of Inertia
  • Bilinear Form on Inner Product Space
  • Cayley-Hamilton Theorem
  • Spectral Gap Theorem
 Slides
13 Thursday
4/17/2025
  • Isometries of Euclidean Space
 Slides
14 Thursday
4/24/2025
  • Affine Geometry
 Slides
15 Thursday
5/1/2025
  • Categories and Functors in Linear Algebra
 Slides
16 Thursday
5/8/2025
5-7:30pm		 Final Exam 2MTC 825