Greetings! This website contains the official handouts for Linear Transformations, a presentation by Carlo Angiuli to close off second semester. The goal of this presentation is to explore abstract linear transformations, and show how they provide a geometric interpretation of the matrix theory previously learned.
1: Definitions / Vector Spaces
2: Matrices / Huh?
3: Let's Compute! / Cool! What else can I do?
4: Inverses? / Wait, multiplying rectangular matrices?
5: Dimension
6: Rank and Nullity / Rank-Nullity Theorem
7: Orthogonal Complements / Results! / The Importance of Conceptual Thinking
8: Determinants / Some Properties of Determinants
9: Zero Determinants / Summary of Properties of Zero Determinants
10: Eigenvectors / Diagonalization
11: Similarity / Similarity Invariants / Isomorphism