Lectures related to Untitled | EPFL Graph Search

Linear Independence and Basis

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

Linear Algebra: Subspaces and Transformations

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

Linear Algebra: Vector Spaces

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

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Linear Applications and Matrices MOOC: Linear Algebra (Part 2)

Delves into the bijection between linear applications and matrices, exploring linearity, injectivity, surjectivity, and the consequences of this relationship.

Smooth Manifolds: Diffeomorphisms MOOC: Introduction to optimization on smooth manifolds: first order methods

Explores smooth manifolds through diffeomorphisms and embedded submanifolds in a linear space.

Linear Mapping Basics Log in to Mediaspace to watch this video

Covers the basics of linear mapping and coordinate systems.

Linear Algebra: Lecture Notes Log in to Mediaspace to watch this video

Covers determining vector spaces, calculating kernels and images, defining bases, and discussing subspaces and vector spaces.

Dimension Theory of Rings Log in to Mediaspace to watch this video

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Linear Applications: Matrices and Transformations Log in to Mediaspace to watch this video

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

Orthogonality and Projection Log in to Mediaspace to watch this video

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Linear Algebra: Vector Spaces and Linear Independence Log in to Mediaspace to watch this video

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

Linear Independence and Bases Log in to Mediaspace to watch this video

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

Tensor Products and Symmetric Power Log in to Mediaspace to watch this video

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Physics 1: Harmonic Oscillator and Spherical Coordinates Log in to Mediaspace to watch this video

Explores harmonic oscillators, pendulum movement, and spherical coordinates in physics.

Dimension theory of rings Log in to Mediaspace to watch this video

Covers the dimension theory of rings, including additivity of dimension and height, Krull's Hauptidealsatz, and the height of general complete intersections.

Polynomials on a Field: Basics and Operations Log in to Mediaspace to watch this video

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Linear Transformations: Polynomials and Bases Log in to Mediaspace to watch this video

Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

Linear Algebra: Systems and Subspaces Log in to Mediaspace to watch this video

Covers linear systems, vector subspaces, and the kernel and image of linear applications.

Vector Spaces Equivalence Log in to Mediaspace to watch this video

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