Lectures related to Degree of an algebraic variety

Matrix Similarity and Diagonalization

Explores matrix similarity, eigenvalues, and diagonalization in linear algebra.

Algebraic Multiplicity, Geometric Multiplicity

Explores algebraic and geometric multiplicities of eigenvalues in linear algebra.

Characteristic Polynomials and Similar Matrices

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

Diagonalization: Examples

Explores examples of diagonalization in linear algebra, focusing on eigenvalues and eigenvectors.

Intersection Numbers: Algebraic Counting Solutions

Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.

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Curve of Genus 2: Very Ample Divisors

Explores very ample divisors on curves of genus 2 and their implications.

Symmetric Matrices and Eigenvalues

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

Linear Algebra: Cofactors and Eigenvectors

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

Characteristic Polynomial and Similar Matrices

Covers characteristic polynomials, similar matrices, eigenvalues, and algebraic multiplicities.

Diagonalization of Matrices: Eigenvectors and Eigenvalues

Covers the concept of diagonalization of matrices through the study of eigenvectors and eigenvalues.

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Diagonalization of Matrices

Explores diagonalizable matrices, eigenvectors, and population dynamics using concrete examples and matrix operations.

Diagonalization: multiplicities

Explores geometric and algebraic multiplicities in diagonalization of linear transformations.

Diagonalization of Matrices

Explores the diagonalizability of matrices, linear transformations, and matrix representations with practical examples.

Diagonalization of Matrices

Explores the diagonalization of matrices through eigenvectors and eigenvalues.

Eigenvalues and Eigenvectors: Polynomials and Matrices

Explores eigenvalues, eigenvectors, and characteristic polynomials of matrices, emphasizing their importance in matrix operations.

Linear Systems: Equilibria and Stability

Explores linear systems' equilibria, stability, and modes, including Lyapunov stability and exponential stability.