Linear Algebra: Matrix Representation

Related lectures (50)

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

Covers linear transformations, matrices, kernels, and properties of invertible matrices.

Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.

Covers vector spaces, bases, and decomposition of vectors in R³.

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

Covers the reduction of a linear application and finding corresponding reduced forms and bases.

Explores the canonical basis in linear algebra, focusing on matrix representation, diagonalizability, and characteristic polynomials.

Explores vector spaces, subspaces, bases, and linear combinations in R² and R³, including free and linked families.

Explains linear independence, basis, and matrix rank with examples and exercises.

Explores matrix representations of linear maps and their invariance, using examples and special cases.

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

Explores the scalar product of vectors, including properties and calculation methods.

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

Covers the basics of linear mapping and coordinate systems.

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

Explains orthogonal families, bases, and projections in vector spaces.

Covers landmarks, coordinate systems, frames, and terminology in coordinates, emphasizing geometric angles and orthogonal vectors.

Covers the theorems related to orthogonal projection and orthonormal bases.

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

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