Lectures related to Linear Transformations: Matrices and Applications

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

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

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

Explores linear transformations, matrices, kernels, and images in algebra.

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

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

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

Explores injective and surjective linear transformations, kernel, image, and matrix operations.

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

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

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

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

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

Covers the concept of expressing vectors in proper bases and the importance of diagonalization of matrices.

Explains orthogonal projection in linear algebra, focusing on transforming non-orthogonal bases into orthogonal ones.

Explores linear algebra fundamentals, including key definitions, theorems, and practical applications in mathematics and technology.

Explores vector space operations, linear transformations, matrix representation, and linear applications.

Explores linear dependence and independence of vectors in geometric spaces.

Covers parametric to Cartesian representation, linear independence, bases, linear transformations, and linear applications.

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