WildLinAlg12: Generalized dilations and eigenvectors

This video introduces the important idea of changing coordinates in Linear Algebra. A linear transformation can be described using many different matrices, depending on the underlying coordinate system, or ordered basis, which is used to describe the space.

The simplest case is when the linear transformation is in diagonal form. Finding such a diagonal form requires finding the eigenvalues and eigenvectors of a matrix, which we introduce in this video. We also discuss change of basis matrices.

This is the 12th video in a first course of Linear Algebra given by N J Wildberger of the School of Mathematics and Statistics at UNSW. NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning and using trigonometry---see his WildTrig YouTube series under user `njwildberger'. There you can also find his series on Algebraic Topology, History of Mathematics and Universal Hyperbolic Geometry.

[lavc]

from 1990 up to now I have been taking this class in diff countries, and finally I got it here.I passed the class with C but I did not no what we are doing?and why we do all these calculations.thank you Real Teacher.

[adriancox]

A great video here and very in depth. I now have a better understanding of what I have been doing when I have found eigenvectors. I have used this on the coefficients of second degree polynomials to find out what type of quadric the polynomial gives. I am now tempted to have another look at this.

[saadamehdi]

I can't get why A sub b is not equal to C(sub r to b) * A(sub r)