Description
This is the ninth lecture of this course on
Linear Algebra. Here we give a gentle introduction to three dimensional
space, starting with the analog of a grid plane built from a packing of
parallelopipeds in space.
We discuss two different ways of drawing 3D objects in 2D, emphasizing
the importance of parallel projection. Some discussion of the nature of
space and modern physics, then an introduction of affine space via
coordinates. The distinctions between points and vectors is important,
and we talk also about lines and planes.
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