Mathématiques
350 documents à télécharger gratuitement
Cours, examens, TD, TP et exercices de mathématiques. Thèmes couverts : algèbre, analyse, probabilités, statistique, optimisation.
This document discusses normal sets in the context of a function between power sets. It provides a series of problems to demonstrate and deduce properties of these normal sets. The problems culminate in establishing bijections under certain conditions.
Ce document traite des espaces vectoriels normés, en fournissant des définitions de normes et des propriétés associées. Il explore également les distances associées à une norme et les différents types de normes courantes. L'importance des limites et de la continuité dans un espace vectoriel normé est également abordée.
This document discusses obtuse and acute families of vectors in an Euclidean space. It explores the properties of strictly obtuse and acute families and their implications on vector spaces. The document includes proofs and constructions related to these concepts.
This document presents a series of mathematical exercises focusing on symmetric and orthogonal matrices. Each exercise addresses essential properties and relationships involving these matrices, such as eigenvalues and their implications. Solutions and indications for each exercise are provided to guide the understanding of the concepts involved.
This document presents a series of mathematical exercises focused on symmetric and orthogonal matrices. It includes definitions, proofs, and properties of these matrices. The aim is to enhance understanding of matrix algebra and its applications.
This document contains exercises focused on the diagonalization of matrices. Each exercise presents a matrix and requires the reader to find its diagonal form or provide conditions for diagonalizability. Solutions and indications for each exercise are also provided.
Ce document contient une série d'exercices sur les espaces euclidiens, incluant des problèmes sur les endomorphismes et les projections orthogonales. Chaque exercice est accompagné d'indications pour guider la résolution. Les exercices sont destinés à évaluer la compréhension des concepts mathématiques avancés.
This document presents a series of mathematical problems related to translations of functions in a vector space. The problems require the verification of properties such as the dimensionality of the space generated by translations and the characterization of free families using determinants. The document includes detailed questions and proofs related to vector spaces of infinitely differentiable functions.
This document presents a series of mathematical problems related to Hankel determinants. It includes definitions, theorems, and proofs regarding the properties of these determinants and their relationships with linear algebra concepts. The document is structured in multiple parts, each addressing different aspects of the topic.
This document contains a series of mathematical exercises focusing on real Hilbert spaces. It includes problem statements and indications for the solutions of each exercise, covering aspects like orthogonality, projections, and polynomial properties. Solutions to the exercises are also provided to assist learners.
Ce document contient une série d'exercices portant sur les espaces préhilbertiens, avec des énoncés de problèmes variés nécessitant des démonstrations et des applications de concepts mathématiques. Chaque exercice est accompagné d'indications et de corrigés pour aider à la compréhension des solutions.
This document contains a mathematics exam with four exercises covering concepts such as affine transformations, intersection of planes in 3D space, sequences, and partial differential equations. Each exercise asks students to solve problems related to these mathematical topics and provide proofs or demonstrations as necessary.
This document contains a mathematics exam focusing on differential equations and linear algebra concepts. It involves proving properties of solutions to differential equations, matrix calculations, and exploring vector spaces. The exam is structured into exercises and problems that require both theoretical and practical mathematical skills.
This document consists of a series of mathematics exercises focused on determinants of order n, including calculation techniques and theoretical proofs. Each exercise is accompanied by hints and corrections to guide students in their understanding of the concepts presented. The content is geared towards deepening knowledge in determinants and their properties.
This chapter discusses the concepts of adjoint operators and self-adjoint endomorphisms in Euclidean vector spaces. It covers definitions, properties, and characterizations related to these mathematical entities. Additionally, it explores the implications of these properties on projection operators and positive definite mappings.
Ce chapitre traite des systèmes différentiels linéaires à coefficients constants, incluant leur définition, écriture matricielle et propriétés. Il propose également des exercices sur la résolution pratique de tels systèmes. Une attention particulière est portée sur les cas où la matrice est diagonalisable et les implications concernant les solutions.
This document covers various properties and definitions related to endomorphisms in vector spaces, focusing on diagonalization, eigenvalues, and characteristic polynomials. It outlines general principles including conditions for diagonalizability and relationships between polynomials and linear operators. The content is aimed at advanced students in mathematics, particularly in the context of higher education.
This document contains a set of exercises focused on determinants of matrices of order n. It challenges students to prove various properties related to determinants, including conditions for invertibility and results involving antisymmetric matrices. Each exercise comes with indications and corrections to guide students through the problem-solving process.
This document contains exercises focused on the calculation of determinants of order 3. Each exercise provides matrices with specific elements to find their determinants. Additionally, detailed indications and corrections are given for each exercise.
Ce document aborde les problèmes liés aux entiers algébriques et la loi de réciprocité quadratique. Il contient des démonstrations et des équivalences concernant les polynômes et les endomorphismes dans des corps de nombres. En outre, il explore les propriétés des corps quadratiques et leurs automorphismes.
Ce document traite des systèmes d'équations algébriques linéaires et des matrices. Il présente les techniques fondamentales pour résoudre ces systèmes et aborde les concepts de rang, de déterminant et d'applications linéaires. Des notions sur les espaces euclidiens et les opérateurs linéaires sont également discutées.
Ce document traite des nappes paramétrées en géométrie, explorant leurs propriétés affines et métriques. Il couvre également des concepts liés aux arcs paramétrés, à la rectification, et aux points réguliers de surfaces. Des définitions fondamentales et des exemples illustrés sont présentés pour une compréhension approfondie.
This document covers fundamentals of numerical and vector series in mathematics. It discusses generalities, the vector space of series, convergence criteria, and significant theorems related to series. The content is structured in a systematic approach for academic purposes.
This document covers the fundamentals of General Algebra, focusing on Groups. It provides definitions, examples, and essential properties of groups and their operations. The material also includes discussions on subgroups, morphisms, and the action of a group on a set.