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 10 - Equations in Lines and Planes in 3D |
In this lecture we discuss parametric and Cartesian equations of lines and planes in 3 dimensional affine space. We start by reviewing lines in 2D. A novel feature is the description of all such lines as a Mobius band. For lines and planes in 3D, we avoid the use of inner products and cross products, using determinants instead.
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