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 08 - Inverting 3x3 Matrices |
Here we solve the most fundamental problem in the subject in the 3x3 case - in such a way that extension to higher dimensions becomes almost obvious. What is the fundamental problem? It is: How to invert a linear change of coordinates? Or in matrix terms: How to find the inverse of a matrix? And the answer rests squarely on the wonderful function called the determinant.
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