Complex Numbers: Notations and Operations

Matrix Calculations: Basis Change and Extensions

Covers matrix calculations, basis change, field extensions, complex numbers modulus, and polar decomposition.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Covers the basics of linear algebra, including matrix operations and singular value decomposition.

Complex Numbers: Definitions and Properties

Covers the definitions and properties of complex numbers, including the field of complex numbers, the conjugate, the real and imaginary parts, algebraic form, modulus, and argument.

SVD: Singular Value Decomposition

Covers the concept of Singular Value Decomposition (SVD) for compressing information in matrices and images.