MATH-GA2120 Linear Algebra II Spring 2024 Calendar
Week Date Topics Links
1 Wednesday
1/24/2024
  • 1.1: Vector Spaces
  • 1.2: Basis of Vector Space
  • Abstract Notation
  • 2.8: Change of Bases Formulas
  • 1.3: Linear Transformations
  • 1.4: Vector Space of Linear Transformations
  • 1.7: Subspaces
  • 2.7: Fundamental Subspaces of Linear Transformation
  • Normal form of a Linear Transformation
  • Rank-Nullity Theorem
 Slides
2 Wednesday
1/31/2024
  • 1.5: Composition is Matrix Multiplication
  • 3.2: Properties of Determinant
  • 3.4: Determinant of Matrix
  • Determinant of Linear Transformation
 Slides
3 Wednesday
2/7/2024
  • 4.1: Eigenvalues, eigenvectors
  • 4.1: Characteristic Polynomial
  • 4.1: Triangular Matrices
 Slides
4 Wednesday
2/14/2024
  • 4.2: Diagonalizable Linear Transformations
  • 5.1: Inner Product on \(\mathbb{F}^n\)
  • 5.1: Inner Product on Abstract Vector Space
  • 5.1: Cauchy-Schwarz Inequality
 Slides
5 Wednesday
2/21/2024
  • 5.1: Inner Product Spaces
  • 5.2: Orthogonality
  • 5.3: Orthogonal Projection
  • 5.4: Least Squares Fit
 Slides
6 Wednesday
2/28/2024
  • 5.5: Adjoint Transformation
  • 5.6: Isometries and Unitary Operators
 Slides
7 Wednesday
3/6/2024
  • Unitary Basis
  • Adjoint of Linear Map
  • Unitary Maps and Matrices
  • 6.1: Schur Representation
 Slides
8 Wednesday
3/13/2024
    Canceled
9 Wednesday
3/20/2024		 No class  
10 Wednesday
3/27/2024
  • Self-Adjoint Maps and Matrices
  • Positive Definite Self-Adjoint Maps
  • Singular Value Decomposition
 Slides
11 Wednesday
4/3/2024
  • 6.3: Polar Decompositions
  • Moore-Penrose Pseudoinverse
 Slides
12 Wednesday
4/10/2024
  • Linear Transformation of Ball is Ellipsoid
  • Operator Norm of Linear Map
  • Frobenius Norm of Linear Map
  • Condition Number of Linear Map
 Slides
13 Wednesday
4/17/2024
  • Bilinear and Sesquilinear Forms
  • Quadratic Forms
 Slides
14 Wednesday
4/24/2024
  • Diagonalization of Quadratic Form
  • Sylvester's Law of Inertia
  • Cayley-Hamilton Theorem
 Slides
15 Wednesday
5/1/2024
  • Chapter 9: Advanced Spectral Theory
16 Wednesday
May 8, 2024
6-7:50pm		 Final Exam Warren Weaver Hall 517