Lectures related to Schur's Lemmas, Part 2

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

Explores linear dependence and independence of vectors in geometric spaces.

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

Covers the basics of linear algebra, emphasizing the identification of subspaces through key properties.

Explores operations and applications of linear algebra in solving equations and transformations.

Covers the properties of vectors, including commutativity, distributivity, and linearity.

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

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

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

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

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Covers Dirac's notation in linear algebra and the tensor product concept in Hilbert spaces.

Explores changing bases in linear algebra in 3 dimensions, focusing on matrix transformations and vector representations.

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

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

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

Explores vector spaces, linear independence, and spanning sets in linear algebra.

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

Explores linear dependence theorems and proofs, emphasizing the importance of understanding linear dependence in linear algebra.

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