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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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Related publications (82)

Related courses (446)

Lectures in this MOOC (145)

Related concepts (417)

Instructors (2)

MATH-506: Topology IV.b - cohomology rings

Singular cohomology is defined by dualizing the singular chain complex for spaces. We will study its basic properties, see how it acquires a multiplicative structure and becomes a graded commutative a

MATH-111(e): 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.

Let k be an algebraically closed field of arbitrary characteristic, let G be a simple simply connected linear algebraic group and let V be a rational irreducible tensor-indecomposable finite-dimension

Let G be a simple algebraic group over an algebraically closed field F of characteristic p >= h, the Coxeter number of G. We observe an easy 'recursion formula' for computing the Jantzen sum formula o

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.

Finding Orthogonal/Orthonormal Base: First Step

Introduces the first step in finding an orthogonal/orthonormal base in a vector space.

Linear Applications: Some Basic Concepts

Introduces the basic concepts of linear applications, including injective, surjective, and bijective functions, along with function composition.

Elementary Operations: Matrix Version

Covers elementary operations in matrix form, matrix size, component notation, equality, augmented matrices, and row operations.

Complex Eigenvalues Appendix

Covers the factorization of polynomials with complex coefficients and diagonalizability of matrices.

Diagonalisation of Symmetric Matrix by Orthogonal Matrix

Covers the method of diagonalizing a symmetric matrix using an orthogonal matrix.

The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of compl