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Concept

Multiplicity (mathematics)

Related lectures (27)

Algebraic Multiplicity, Geometric Multiplicity MOOC: Linear Algebra (Part 2)

Explores algebraic and geometric multiplicities of eigenvalues in linear algebra.

Isogeny Graphs: Eigenvalues and Cryptography

Explores isogeny graphs of supersingular elliptic curves, showing optimal mixing times for random walks and applications to cryptography.

Multistep methods

Covers multistep methods for solving differential equations, focusing on stability conditions and examples.

Untitled

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Symmetric Matrices and Eigenvalues MOOC: Linear Algebra (Part 3)

Explores symmetric matrices, eigenvalues, and characteristic polynomials in matrix analysis.

Diagonalizability Criterion MOOC: Linear Algebra (Part 2)

Covers the criterion for diagonalizability of matrices, focusing on comparing examples and understanding the relationship between algebraic and geometric multiplicities of eigenvalues.

Linear Recurrence Relations: Solving Techniques

Explores linear homogeneous recurrence relations, solving techniques, characteristic equations, and examples like Fibonacci numbers.

Untitled

Solutions of Homogeneous Linear Differential Equations Log in to Mediaspace to watch this video

Covers the solutions of homogeneous linear differential equations and how to find linearly independent solutions.

Characteristic Polynomials and Similar Matrices Log in to Mediaspace to watch this video

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Linear Differential Equations Log in to Mediaspace to watch this video

Explores solving linear differential equations and the principle of superposition with illustrative examples.

Projective Plane Curves Log in to Mediaspace to watch this video

Introduces projective plane curves, degrees, components, multiplicities, intersection numbers, tangents, and multiple points, culminating in the statement of Bézout's theorem and its consequences.

Principle of Superposition in Differential Equations Log in to Mediaspace to watch this video

Explores the principle of superposition in differential equations and the fundamental theorem of algebra.

Polynomial Equations: Determining Coefficients Log in to Mediaspace to watch this video

Covers the process of determining coefficients in polynomial equations.

Characteristic Polynomials: Solutions and Roots Log in to Mediaspace to watch this video

Covers characteristic polynomials, their solutions, and roots for different types of polynomials.

Affine Plane Curves Log in to Mediaspace to watch this video

Covers the study of affine plane curves and their properties, including the concept of multiplicity and its applications.

Tangent Lines and Equality Log in to Mediaspace to watch this video

Explores the intersection multiplicity of curves and the absence of common tangent lines.

Local Rings and Residues Log in to Mediaspace to watch this video

Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.

Linear Algebra: Cofactors and Eigenvectors Log in to Mediaspace to watch this video

Explains cofactors, eigenvectors, eigenvalues, and studying linear applications.