Decomposition and Separability

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Covers homomorphisms, algebraic extensions, cutting, splitting, and separable elements in Fok [x].

Covers the concept of finite degree extensions in Galois theory, focusing on separable extensions.

Covers the QR factorization method applied to solving a system of linear equations in the least squares sense.

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

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

Covers advanced topics in volume calculations, focusing on decomposing and composing domains.

Explores algebraic decomposition, simple structures, irreducibility, and separability in finite degrees.

Covers complete and orthonormal families in a Hilbert space, discussing unique projections and vector decomposition.

Explores complex roots, conjugate pairs, and quadratic equations solving strategies.