Lectures related to Untitled | EPFL Graph Search

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

Linear Algebra: Matrices and Vector Spaces

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

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Vector Spaces: Bases and Dimension

Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.

Singular Value Decomposition: Applications and Interpretation

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

Linear Algebra: Vector Spaces

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

Linear Independence and Bases

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

Linear Algebra: Linear Dependence and Independence

Explores linear dependence and independence of vectors in geometric spaces.

Linear Codes: Systematic vs Non-Systematic

Explores the creation of systematic linear codes and the transformation of non-systematic codes, showcasing their equivalence and importance in simplifying encoding and decoding processes.

Linear Mapping Basics

Covers the basics of linear mapping and coordinate systems.

Linear Combinations and Basis Characterization

Explores linear combinations, basis determination, and vector space dimensionality through practical examples and exercises.

Linear Algebra: Vector Spaces and Linear Independence

Covers vector spaces, operations, and linear independence with examples from polynomials and functions.

Untitled

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Linear Independence and Bases in Vector Spaces

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

Analytical Study of Space

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

Linear Independence in Vector Spaces

Explores linear independence in vector spaces and the concept of bases.

Vector Subspaces in R4

Explores vector subspaces in R4, symmetric matrices, basis vectors, and canonical forms.

Linear Dependence and Independence

Explores linear dependence and independence of vectors, including subspaces generation and corollaries.

Linear Algebra: Subspaces and Transformations

Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.