Complex Numbers: Notations and Operations

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Related lectures (24)

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Matrix Calculations: Basis Change and Extensions

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

Harmonic Forms: Main Theorem

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

Linear Algebra Review

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.

Complex Numbers: Definitions and Properties

Covers the definitions and properties of complex numbers, including conjugate and modulus.

Integration of Rational Functions

Covers the integration of rational functions and the decomposition into irreducible factors.

Linear Systems: Diagonal and Triangular Matrices, LU Factorization

Covers linear systems, diagonal and triangular matrices, and LU factorization.

Characterization of Invertible Matrices

Explores the properties of invertible matrices, including unique solutions and linear independence.

Singular Value Decomposition: Applications and Interpretation

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.