Change of Basis and Taylor Coefficient Vectors - Wild Linear Algebra A - NJ Wildberger

Explore the concept of change of basis and Taylor coefficient vectors in linear algebra. Delve into the novel idea of a vatrix, a matrix with vector entries, and its application in encoding vector space bases. Learn how to represent coefficient vectors as row vectors and understand the intuitive labelling of change of basis matrices. Examine practical examples, including Bob and Rachel's affine plane bases and Taylor coefficient vectors for polynomials. Discover the connection between generalized Pascal matrices and change of basis, forming a one-parameter group with interesting algebraic properties. This advanced lecture provides a comprehensive framework for understanding coordinate vectors and their applications in calculus, offering valuable insights for students of mathematics and related fields.

Introduction
Two kinds of linear relations
Augmented matrix algebra
Bob and Rachel
Change of basis
Change of basis matrix
Exercise
Calculus
Relation between vectors
Generalized Pascal matrix
Taylor coefficient translation theorem