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MTHS 632
Linear Algebra through Geometry

Adam Fieldsteel

Textbook
T. Banchoff and J. Wermer, Linear Algebra through Geometry (Springer), 2nd edition
Course Schedule
I. Linear algebra in the plane

1. Basic operations on vectors in the plane
2. Linear independence of vectors, basis vectors
3. Connections between algebraic operations on vectors and geometric quantities
4. Solutions of 2-by-2 systems of linear equations
5. Linear transformations of the plane and  matrix operations
6. Determinants and area
7. Characteristic polynomials and eigenvectors for 2-by-2 matrices
II. Linear algebra in 3 and higher dimensions

1. We will systematically extend all of the above algebraic and geometric ideas to the setting of vectors in 3-space.
2. We will briefly consider the extension of the above ideas to dimensions greater than 3.