Linear Algebra
University, second course50 min / week · one to one
Saturdays at 1:30 PMnext on Sat 17 Oct, 1:30 PM
Linear algebra worked straight through Serge Lang's Linear Algebra, the Yale text in the Undergraduate Texts in Mathematics series. Lang is explicit in his foreword that this is a second course. It assumes you have…
- Vector spaces: bases, dimension, sums and direct sums
- Matrices, linear equations and matrix multiplication
- Linear mappings: kernel, image, composition and inverses
- Scalar products, orthogonal bases, quadratic forms and Sylvester's theorem
- Determinants, Cramer's rule and rank from subdeterminants
- Eigenvectors, eigenvalues and the characteristic polynomial
- Symmetric, hermitian and unitary operators and the spectral theorem
- Triangulation, Hamilton Cayley and the Jordan normal form
- Convex sets, separating hyperplanes and Krein Milman
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