MFCS

14 March -- 2022

Tentative Schedule

• Lecture 1: Overview
• Lecture 2: Theory of matrices -- basic matrix operations from the point of system of linear equations.
• Lecture 3: Combinatorial interpretation of matrix operations, Interpretations of Determinant.
• Lecture 4: Multilinear definition of Determinant.
• Lecture 5: Combinatorial interpretation.
• Lecture 6: Combinatorial proof of Cayley-Hamilton and combinatorially computing the determinant using clows.
• Lecture 7: Inner products, Norms, Orthogonality, Gram-Schmidt Orthogonalization (QR factorization).

References

Books and Papers

• Brualdi-Ryser.
• Trefethen-Bau.

Homework

• Homework 1: Due Date 16 Sept.
• Homework 1: Due Date 21 Oct.