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 22 - Polynomials and Sequence Spaces |
Polynomials can be interpreted as functions, and also as sequences. In this lecture we move to considering sequences. Aside from the familiar powers, we introduce also falling and rising powers, using the notation of D. Knuth. These have an intimate connection to forward and backward difference operators. We look at some particular sequences, such as the square pyramidal numbers, from the view of this 'difference calculus'.
Go to the Course Home or watch other lectures: