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 07 - More Applications of 2x2 Matrices |
We continue discussing 2x2 matrices, their interpretation as linear transformations of the plane, how to analyse rotations, including a rational formulation, and how to combine rotations and reflections. Finally we discuss the connections with calculus, introducing the idea that the derivative is really a linear transformation.
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