Monday |
Wednesday |
Friday |
| Jan. 26 Lecture #1: Vector Spaces Fields Complex Numbers |
Jan. 28 Lecture #2: Example of Vector Spaces Subspaces Homework Due: Homework #1: Homework Assignment |
Jan. 30 Lecture #3: Subspaces in Calculus Sum of Subspaces |
| Feb. 2 Lecture #4: Direct Sums |
Feb. 4 Lecture #5: Span Linear Independence Bases Homework Due: Homework #2: Homework Assignment |
Feb. 6 Quiz #1 Lecture #6: Dimension |
| Feb. 9 No class |
Feb. 11 Lecture #7: Dimension of Sum (video) Homework Due: Homework #3: Homework Assignment |
Feb. 13 Lecture #8: Linear Transformations |
| Feb. 16 Lecture #9: Vector Space of Linear Transformations Range and Null Space |
Feb. 18 Lecture #10: Products of Linear Maps Matrices of Transformations Homework Due: Homework #4: Homework Assignment |
Feb. 20 Quiz #2 Lecture #11: Proof writing primer |
| Feb. 23 Lecture #12: Properties of Matrices |
Feb. 25 Lecture #13: LU Decomposition Inplace LU Decomposition Homework Due: Homework #5: Homework Assignment |
Feb. 27 Quiz #3 Lecture #14: LUP Decomposition |
| March 2 Lecture #15: LUP Decomposition Partial Pivoting Computing Derivatives |
March 4 Lecture #16: Polynomials Homework Due: Homework #6: Homework Assignment |
March 6 Quiz #4 Lecture #17: Fundamental Theorem of Algebra Complex Algebra |
| March 9 Lecture #18: Proof of Fundamental Theorem of Algebra |
March 11 Lecture #19: Polynomials of operators Invariant subspaces Homework Due: Homework #7: Homework Assignment |
March 13 Exam 1 Chapters 1-4 Homework 1-7 |
| March 16 Lecture #20: Null(p(T)) One Dimensional Invariant Subspaces |
March 18 Lecture #21: Eigenvalues Linear Independence of Eigenvectors Homework Due: Homework #8: Homework Assignment |
March 20 Quiz #5 Lecture #22: Annihilating polynomial |
| March 23 Lecture #23: Minimal Polynomials Existence of Eigenvalues |
March 25 Lecture #24: Degree of minimal polynomial Eigenbasis Homework Due: Homework #9: Homework Assignment |
March 27 Lecture #25: Eigenbasis Example |
| March 30 Spring Break |
April 1 Spring Break |
April 3 Spring Break |
| April 6 Spring Break |
April 8 Lecture #26: Diagonalization Characterization Homework Due: Homework #10: Homework Assignment |
April 10 Quiz #6 Lecture #27: Minimum Polynomial and Diagonalizability. |
| April 13 Lecture #28: Norms Inner Products |
April 15 Lecture #29: Orthogonal Vectors Pythagorean Theorem Cauchy-Swartz Inequality Homework Due: Homework #11: Homework Assignment |
April 17 Exam 2 Topics Chapter 4 and 5 |
| April 20 Lecture #30: Orthonormal Basis |
April 22 Lecture #31: Gram–Schmidt process Orthogonal complements Homework Due: Homework #12: Homework Assignment |
April 24 Quiz #7 Lecture #32: Orthogonal Projections |
| April 27 Lecture #33: Riesz Representation Theorem |
April 29 Lecture #34: Project 1 Project 2 Adjoint of a Transformation Homework Due: Homework #13: Homework Assignment |
May 1 Lecture #35: Project 3 Adjoint of a Matrix Conjugate Transpose |
| May 4 Lecture #36: Project 4 Self-adjoint Transformation Eigenvalues of a Self-adjoint Transformation |
May 6 Lecture #37: Project 5 Diagonalizability of Self-adjoint Transformations Unitary Matrices Homework Due: Homework #14: Homework Assignment |
May 8 Lecture #38: Project 6 Orthonormal Triangularization Algebraic multiplicity of an Eigenvalue Characteristic Polynomial Cayley-Hamilton Theorem |
| May 11 Quiz #8 Lecture #39: Jordan Canonical Form |
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