Handouts for Math 223

Extra Credit Offer:  If you find an error in any handout, let me know. If you are the first to report it, you will get some extra credit on quizzes. This includes errors in spelling and grammar, but mathematical errors will be worth more.

Important:  Expectations for group work and writing. 

Exams from previous semesters

Two Types of Projections

A Concrete Problem Worked Abstractly: Angles in a Tetrahedron using a Coordinate-Free Approach

Comments on the Gram-Schmidt Process and Projections

Properties Equivalent to Invertibility
Twenty-one things about a matrix that are equivalent to invertibility.

Linear Functions, Independence, and Spanning
Some things you should be able to prove.

Bases, Coordinates, Linear Maps, and Matrices
What happens to coordinates and the matrix of a linear transformation when you change bases.
Similar to Section 6.5 of Messer, and Sections 5.3 and 5.4 of Schneider.

A Theorem on Column Spaces, Supplement to Section 6.6 of Messer

The Principle of Mathematical Induction

Uses of Eigenvectors and Eigenvalues
This is purely for your own interest.