This course covers topics such as calculating the kernel of a matrix, polar form of complex numbers, change of basis, LU decomposition, PLU decomposition, QR decomposition, and Jordan Normal Form. The course aims to teach students how to calculate dimensions and bases of range and kernel, as well as provide an overview and examples of Jordan Normal Form. The teaching method includes examples and transformation matrices. This course is intended for individuals interested in advancing their knowledge of linear algebra.
Overview
Syllabus
Calculating the kernel of a matrix - An example.
Polar form of complex numbers - How to calculate?.
Change of basis - transformation matrices.
Calculating dimension and basis of range and kernel.
LU decomposition - An Example.
PLU decomposition - An Example.
QR decomposition (for square matrices).
Jordan Normal Form - Part 1 - Overview.
Jordan Normal Form - Part 2 - An Example.
Jordan Normal Form - Part 3 - Another Example.
Jordan Normal Form - Part 4 - Transformation Matrix.
A Table You Should Remember (Sine and Cosine).
Taught by
The Bright Side of Mathematics
