Lectures related to Symmetric polynomial

Minimal Polynomials: Uniqueness and Division

Explores the uniqueness of minimal polynomials and the division algorithm for polynomials.

Division Polynomials: Theorems and Applications

Explores division polynomials, theorems, spectral values, and minimal polynomials in endomorphisms and vector spaces.

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Relations in Computer Science

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Calcul de valeurs propres

Covers the calculation of eigenvalues and eigenvectors, emphasizing their significance and applications.

Diophantine Approximation: Minbowski's Theorem

Covers Minbowski's Theorem on Diophantine Approximation and Gram-Schmidt orthogonalization.

Viète Relations: Polynomial Roots and Coefficients

Explores Viète's identities, relating polynomial roots and coefficients to solve equations.

Tensor Products and Symmetric Power

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.

Matrix Diagonalization: Spectral Theorem

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

Eigenvalues and Eigenvectors

Covers eigenvalues, eigenvectors, and their applications in linear algebra.

Polynomial Optimization: SOS and Nonnegative Polynomials

Explores polynomial optimization, emphasizing SOS and nonnegative polynomials, including the representation of polynomials as quadratic functions of monomials.

Vector Spaces and Scalar Products

Covers vector spaces, scalar products, norms, and forms of polarization in standard properties.

Properties of Operations: Equivalence Relations and Logic Basics

Explores properties of operations, equivalence relations, and logic basics.

Determinants: Symmetric Formulas and Properties

Explores symmetric formulas and properties of determinants, including invertibility and matrix calculations.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Minkowski's Theorems: Lattices and Volumes

Explores Minkowski's theorems on lattices, volumes, and set comparisons.

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Polynomials and Endomorphisms

Covers the fundamentals of polynomials, endomorphisms, division, roots, matrices, and algebraic homomorphisms.

Sets: Operations and Relations

Covers set operations and their relations to propositional logic, including cardinality.