MATH 236 Algebra 2

Description
Linear equations over a field. Introduction to vector spaces. Linear mappings. Matrix representation of linear mappings. Determinants. Eigenvectors and eigenvalues. Diagonalizable operators. Cayley-Hamilton theorem. Bilinear and quadratic forms. Inner product spaces, orthogonal diagonalization of symmetric matrices. Canonical forms.
Credits
3.0
Mathematics & Statistics

Vocab list

Subject Semester

Proof strategies and definitions

Winter 2013

Lecture notes

Subject Semester

Monday, January 7, 2013

Introduction to the course

Winter 2013

Tuesday, January 8, 2013

Complex numbers and vector spaces

Winter 2013

Thursday, January 10, 2013

Subspaces and direct sums

Winter 2013

Monday, January 14, 2013

Span and linear independence

Winter 2013

Tuesday, January 15, 2013

Bases

Winter 2013

Thursday, January 17, 2013

Dimension

Winter 2013

Monday, January 21, 2013

Introduction to linear maps

Winter 2013

Tuesday, January 22, 2013

Kernels and images

Winter 2013

Thursday, January 24, 2013

The matrix of a linear map

Winter 2013

Tuesday, January 29, 2013

Inverting linear maps

Winter 2013

Thursday, January 31, 2013

Linear operators and review

Winter 2013

Monday, February 4, 2013

A review of polynomials

Winter 2013

Thursday, February 7, 2013

Polynomials, introduction to eigenvalues

Winter 2013

Monday, February 11, 2013

Eigenvalues and eigenvectors

Winter 2013

Tuesday, February 12, 2013

Matrix representations of linear operators

Winter 2013

Thursday, February 14, 2013

Missed this lecture

Winter 2013

Monday, February 18, 2013

Missed this lecture too

Winter 2013

Tuesday, February 19, 2013

Proposition 5.2.1, review session

Winter 2013

Thursday, February 21, 2013

Introduction to inner product spaces

Winter 2013

Monday, February 25, 2013

Was not there

Winter 2013

Tuesday, February 26, 2013

Gram-Schmidt

Winter 2013

Thursday, February 28, 2013

Midterm

Winter 2013

Monday, March 11, 2013

Orthogonal projections and minimisation

Winter 2013

Tuesday, March 12, 2013

I slept in

Winter 2013

Thursday, March 14, 2013

Operators on inner product spaces

Winter 2013

Course quiz

Subject Semester

Practice questions

Winter 2013

Summary

Subject Semester

Midterm review

Winter 2013

Review questions

Winter 2013

Final review

Winter 2013

HTSEFP

Winter 2013