Advanced Linear Algebra, Spring 2017

Tue 5/16: Last Applications of SVD; Topic review for final.

Thu 5/11: Singular Value Decomposition and Applications.

Tue 5/9: Polar decomposition and singular values.

Thu 5/4: Least Squares for overdetermined systems.

Thu 4/27: Exam 2.

Tue 4/25: Review for Exam (and/or Least Squares).

Thu 4/20: Spectral Theorem for self adjoint and normal operators.

Tue 4/18: Unitary equivalence and diagonalization, Schur’s lemma.

Thu 4/13: Adjoints, Isometries and Unitary operators.

Tue 4/11: Gram-Schmidt Process.

Thu 4/6: Orthogonality and orthonormality.

Tue 4/4: Inner Product Spaces.

Thu 3/23: LU Decomposition.

Tue 3/21: Diagonalization.

Thu 3/16: Diagonalization.

Tue 3/14: Eigenvalues.

Thu 3/9: Exam 1.

Tue 3/7: Cofactor expansion for determinants.

Thu 3/2: Determinants continued.

Tue 2/28: Change of basis, similarity. Determinants.

Thu 2/23: Fundamental subspaces and rank.

Tue 2/21: Pivot analysis, dimension, finding inverses.

Thu 2/16: Quiz 2 solutions.

Solutions to Quiz 2

Thu 2/16: Linear systems of equations and row reduction.

Tue 2/14: Invertibility, Isomorphisms, Subspaces.

Thu 2/9: Quiz 1 solutions.

Solutions to Quiz 1

Thu 2/9: Linear transformations, matrix multiplication.

Tue 2/7: Vector spaces, Bases.

We will have our first quiz Thursday on homework problems from 1.1 and 1.2.