MOOC
Algebra (part 1)
Description
Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.
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Ontological neighbourhood
Instructor
Lectures in this MOOC (145)
Systems of Linear Equations and MatricesMOOC: Algebra (part 1)
Covers the definition and solution of linear equations with real coefficients in 2D and 3D space.
Number of Solutions in Linear SystemsMOOC: Algebra (part 1)
Explores the number of solutions in linear systems of equations and the conditions for no solution, a unique solution, or an infinite number of solutions.
Matrix Operations: Triangular MatricesMOOC: Algebra (part 1)
Explores operations with triangular matrices and their role in solving linear systems.
Linear Equations and Matrices: Solution Methods, Elementary OperationsMOOC: Algebra (part 1)
Explores solution methods and elementary operations for linear equations and matrices, demonstrating techniques to simplify systems and obtain solutions.
Elementary Operations: Matrix VersionMOOC: Algebra (part 1)
Covers elementary operations in matrix form, matrix size, component notation, equality, augmented matrices, and row operations.
Related concepts (402)
Matrix (mathematics)
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.
Vector space
In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied ("scaled") by numbers called scalars. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. The terms real vector space and complex vector space are often used to specify the nature of the scalars: real coordinate space or complex coordinate space.
Invertible matrix
In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular, nondegenerate or (rarely used) regular), if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A−1. Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.
Related courses (475)
MATH-111(e): Linear Algebra
L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et ses applications.
MATH-111(a): Linear Algebra
L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et ses applications.
MATH-115(b): Advanced linear algebra II
L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et de démontrer rigoureusement les résultats principaux du sujet.
Related publications (1,000)
Spectral Estimators for High-Dimensional Matrix Inference
A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...
EPFL2024Randomized low-rank approximation and its applications
In this thesis we will present and analyze randomized algorithms for numerical linear algebra problems. An important theme in this thesis is randomized low-rank approximation. In particular, we will study randomized low-rank approximation of matrix functio ...
EPFL2024SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION
Daniel Kressner, Alice Cortinovis
This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...
Siam Publications2024