WildLinAlg: A first course in Linear Algebra
WildLinAlg: A first course in Linear Algebra
Episodes
Episodes of WildLinAlg
Mark All
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, hopefu
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
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 planes in 3 dimensional space are then studied and drawn, including both Cartesian and parame
Row reduction or Gaussian elimination solves a system of linear equations in stages, by continually combining the equations to successively simplify the system by eliminating variables. We frame the algorithm using the augemented matrix of the
We continue discussing 2x2 matrices, their interpretation aslinear transformations of the plane, how to analyse rotations,including a rational formulation, and how to combine rotations andreflections.Finally we discuss the connections with
This is the 8th lecture in thisseries on Linear Algebra. Here we solve the most fundamental problem inthe subject in the 3x3 case---in such a way that extension to higherdimensions becomes almost obvious. What is the fundamental problem? It
This is the ninth lecture of this course onLinear Algebra. Here we give a gentle introduction to three dimensionalspace, starting with the analog of a grid plane built from a packing ofparallelopipeds in space.We discuss two different ways
Vectors are used throughout engineering and physics because their arithmetic parallels the standard ways of combining force, velocity, acceleration, and other quantities. In this video we look at some examples of each of these, and introduce so
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 va
Linear Algebra is the study of affine geometry and its transformations. In this lecture we set up the basic idea of affine geometry in a visual way and introduce the main problem of the subject: how to go from one affine coordinate system to an
This is the fourth lecture in our series on Linear Algebra. Here we introduce area as a determinant, first in two dimensions, then in three. We give a pictorial definition using the affine grid plane, then also a purely algebraic approach using
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