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 19 - Linear Algebra with Polynomials |
Spaces of polynomials provide important applications of linear algebra. Here we introduce polynomials and the associated polynomial functions. Polynomials are vital in interpolation, and we show how this works. Then we explain how regression in statistics can be viewed using our geometric approach to a linear transformation. Finally we discuss the use of 'isomorphism' to relate the space of polynomials up to a certain fixed degree to our more familiar space of column vectors of a certain size.
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