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 18 - The Geometry of a System of Linear Equations |
To a system of m equations in n variables, we can associate an m by n matrix A, and a linear transformation T from n dim space to m dim space. The kernel and rank of this transformation give us geometric insight into whether there are solutions, and if so what the solutions look like.
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