Vectors are directed line segments. They are quite different from points, since they can be added, multiplied by a scalar or number, and subtracted. T...

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 Stat...

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...

Lines in the plane can be characterized by either parametric or Cartesian equations. The space of all such lines is naturally a Mobius band. Lines and...

Row reduction or Gaussian elimination solves a system of linear equations in stages, by continually combining the equations to successively simplify t...

We continue discussing 2x2 matrices, their interpretation as linear transformations of the plane, how to analyse rotations, including a rational formu...

This is the 8th lecture in this series on Linear Algebra. Here we solve the most fundamental problem in the subject in the 3x3 case---in such a way th...

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...