Lectures related to Matrix Equivalence: Definitions and Properties

Covers the concept of discrete symmetries, focusing on the introduction to asymptotic states and S-matrix.

Discusses isometries and orthonormal bases in mathematics.

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

Explores the matrix associated with reciprocal maps and properties of invertible matrices.

Covers the analysis of local extrema and Hessians, focusing on the development of limit notations.

Covers the fundamental concepts of symmetry and group theory.

Covers matrices, linear applications, vector spaces, and bijective functions.

Explores asymptotic states, S-matrix, and operators in quantum field theory, emphasizing the role of discrete symmetries and complete sets of states.

Covers the concept of asymptotic states and S-matrix in quantum field theory, focusing on the evolution of wave packets and the scattering states.

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

Explains the inertia tensor, main axes, principal moments, and balancing of rotating solids.

Explores matrix equivalence theorems for systems of equations and least squares solutions.

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Covers elementary matrices, their properties, and the algorithm to find the inverse of a matrix.

Explains equivalence relations, classes, and partitions in sets.

Explores the concept of symmetry in integrals and matrix elements.

Covers the concept of interesting subspaces related to matrices and the change of basis matrix.

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

Explores orthogonal projections, symmetry of matrices, and their applications.

Explores linear transformations, matrices, and their properties, including surjectivity, injectivity, and symmetry operations.