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 17 - Rank and Nullity of a Linear Transformation |
In this lecture we step up to linear transformations with spaces of more than 3 dimensions, introduce the kernel and the image properties, and the corresponding dimension numbers called nullity and rank. We discuss how to visualize four dimensions in a way that is consistent with our pictures of two and three dimensions.
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