Concept

Rank–nullity theorem

Related lectures (28)

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

Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.

Explains the Rank Theorem for linear applications in 3D space and its implications.

Delves into the Rank Theorem's implications for linear transformations and mappings.

Covers the Rank Theorem in linear algebra, discussing dimensions and linear independence of vector spaces.

Covers the solutions of homogeneous linear differential equations and how to find linearly independent solutions.

Explores the relationship between row and column ranks of matrices and the concept of linearly independent vectors.

Explores observability and controllability in linear systems, emphasizing the significance of input decoupling for observability.

Explains how to calculate the dimension of a kernel of a matrix transpose.

Covers the Rank Theorem in linear algebra, focusing on vector spaces and linear applications.

Covers the concept of Principal Components Analysis, focusing on representing data optimally in a basis.

Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.

Explores the Rank Theorem in linear algebra, covering matrix properties and determinants.

Explores the associated matrix of a linear map, basis formation, and space relationships.

Explores linear applications, vector spaces, kernels, and invertibility in linear algebra.

Covers basic concepts in linear algebra, such as matrices and systems of linear equations, emphasizing the importance of full-rank matrices.

Covers the Singular Value Decomposition (SVD) in detail, including properties of matrices and system linearity.

Covers exercises submission, a test announcement, and the Rank Theorem in linear algebra.

Explores auto-encoders, covering invertibility conditions, projections, and generalized inverses in linear algebra.

Explores the rank theorem, matrix dimensions, and subspaces, illustrating their relationships and implications.