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 05 - Change of Coordinates and Determinants |
We analyse the fundamental problem of inverting a change of coordinates, and give applications to solving a system of two linear equations in two unknowns. And we introduce vectors and matrices in a purely algebraic way. Composing two changes of variable leads to the basic multiplication formula for matrices. This has a close connection with determinants.
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