A First Course in Linear Algebra
A First Course in Linear Algebra (UNSW). Taught by Professor N. J. Wildberger, this course presents a geometrical view to Linear Algebra, with special orientation to applications and understanding of key concepts. The subject naturally sits inside affine geometry, which is the natural setting for vectors. Flexibility in choosing coordinate frameworks is important for understanding the subject. Determinants also play a key role, and these are introduced in the context of multi-vectors in the sense of Grassmann. The course features a careful treatment of polynomial spaces, with applications to Stirling numbers and cubic splines.
| Lecture 12 - Generalized Dilations and Eigenvalues |
We compare Bob and Rachel's coordinate system and learn how to change from one basis to another. We define similar matrices and generalized dilations. Then we look at an example to sketch the basic idea. This leads to the second most important problem in the subject: how to find the eigenvectors and eigenvalues of a matrix.
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