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 04 - Area and Volume |
Here we start with a pictorial treatment of area, then move to an algebraic formulation using bi-vectors. These are two-dimensional versions of vectors introduced in the 1840s by Grassmann. The three dimensional case of volume uses tri-vectors.
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