Dive into a comprehensive 2.5-hour video series exploring key concepts in linear algebra. Learn to calculate matrix kernels, work with complex numbers in polar form, and master change of basis with transformation matrices. Explore dimension and basis calculations for range and kernel, and delve into matrix decompositions including LU, PLU, and QR. Gain a thorough understanding of Jordan Normal Form through multiple examples and transformation matrices. Conclude with a useful table of sine and cosine values to remember for future calculations.
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
