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 20 - Bases of Polynomial Spaces |
This lecture studies spaces of polynomials from a linear algebra point of view. We are especially interested in useful bases of a four dimensional space like P^3: polynomials of degree three or less. We introduce the standard (or power) basis, also the modified Factorial basis. Translations of the corresponding functions yield linear transformations, giving Taylor bases and a purely algebraic definition of the derivative.
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