Linear Algebra - Lecture 38: Complex Numbers and Complex Eigenvalues

We introduce complex numbers as a tool for dealing with matrices that do not have real eigenvalues.

Please leave a comment below if you have any questions, comments, or corrections.

Corrections:
- At 25:21, the eigenvector corresponding to lambda = i should be (i,1), not (-i,1). Similarly, the eigenvector corresponding to lambda = -i should be (-i,1), not (i,1).

Timestamps:
00:00 - 2x2 example with no real eigenvalues
02:53 - Introduction to complex numbers
05:56 - Addition and multiplication
09:02 - Division and the complex conjugate
12:28 - Complex roots of a quadratic (example)
19:51 - The complex plane
22:06 - Complex eigenvalues and eigenvectors (2x2 example)

#linearalgebra #eigenvaluesandeigenvectors #complexnumbers #matrices #math

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