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 21 - More Bases of Polynomial Spaces |
Polynomial spaces are excellent examples of linear spaces. For example, the space of polynomials of degree three or less forms a linear or vector space which we call P^3. In this lecture we look at some more interesting bases of this space: the Lagrange, Chebyshev, Bernstein and Spread polynomial basis.
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