Lectures related to System Equivalence

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

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

Explores properties of 3x3 matrices with real coefficients and determinant calculation methods.

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

Explores polynomial operations, properties, and subspaces in vector spaces.

Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.

Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

Covers the definition and basic operations of matrices, including addition, scalar multiplication, and matrix multiplication.

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

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Covers polynomials, their operations, division theorem, and provides illustrative examples.

Covers controllability and observability in linear systems, discussing necessary conditions and implications of unimodular matrices.

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

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

Covers matrix operations and reduction to echelon form with practical examples.

Explores vector subspaces in R4, symmetric matrices, basis vectors, and canonical forms.