Lectures related to Linear Algebra: Operations and Applications

Introduces eigenspaces in linear algebra through definitions and practical examples of determining eigenspaces for matrices.

Covers linear applications, matrices, transformations, and the principle of superposition.

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.

Explores linear dependence and independence of vectors in geometric spaces.

Explores systems of linear equations, transformations, dilatation, rotation, and cross ratios in linear algebra.

Covers linear independence, bases, and coordinate systems with examples and theorems.

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

Covers exercises on matrices, vectors, and linear systems.

Explores linear algebra over integers, emphasizing solutions to A.x=b equations and Hermite normal form.

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

Explores linear algebra basics, emphasizing matrix representations of transformations and the importance of choosing appropriate bases.

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Explores linear combinations, matrix-vector product, and matrix equation solutions.

Explores the transformation of vectors and tensors, including rotations and representations in quantum physics.

Explores linear combinations of vectors and matrices in Rn, demonstrating geometric interpretations and matrix operations.

Explores systems of equations, vector operations, and geometric interpretations in linear algebra.

Explores the Eigen library for linear algebra, covering vectors, matrices, arrays, memory management, reshaping, and per-component operations.

Covers the definition and use of coordinate systems and applications in bases and linear equations.

Covers matrix operations, coefficients, combinations, and applications in various scenarios.