WildLinAlg2: Geometry with vectors
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Description
Vectors are directed line segments. They are quite different from points, since they can be added, multiplied by a scalar or number, and subtracted. The arithmetic with vectors is very useful in Linear Algebra, and here we use it to describe various standard applications, including affine combinations of two vectors to describe all the points on a line segment or line determined by two vectors. We use vectors to prove that the diagonals of a parallelogram bisect each other, and that the medians of a triangle all meet.
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This is the Introductory lecture to a beginner's course in Algebraic Topology, MATH5665, given by N J Wildberger of the School of Mathematics and Statistics at UNSW in 2010. The course is suitable for 3rd and 4th year mathematics majors, hopefully with some prior knowledge of group theory. Others...
Published 07/27/10
By studying how Bob would view a dilation in Rachel's framework, we are led to the notion of a generalized dilation. Going from one basis to the other involves a 'Change of basis matrix'. We show how these ideas lead naturally to the important concepts of eigenvectors and associated eigenvalues,...
Published 04/16/10