Titre :	Introduction to linear algebra
Type de document :	texte imprimé
Auteurs :	Lee W. Johnson ; R. Dean Riess ; Jimmy T. Arnold
Mention d'édition :	3e éd.
Editeur :	Reading, Mass. : Addison-Wesley
Année de publication :	1993
Importance :	1 v. (534 p.)
Présentation :	ill. (some col.)
Format :	25 cm
ISBN/ISSN/EAN :	978-0-201-56801-1
Note générale :	Includes index
Catégories :	Mathématique
Mots-clés :	Algèbre linéaire
Index. décimale :	512 Algèbre
Résumé :	Cet ouvrage met l'accent à la fois sur le calcul pratique et sur les principes théoriques et se concentre sur l'introduction précoce de la théorie des matrices et des systèmes d'équations linéaires, des concepts élémentaires vectoriels-espace et du problème des valeurs propres. Avec une augmentation progressive du niveau de difficulté, un style d'écriture accessible et l'intégration de MATLAB, ce texte est une excellente introduction pour les étudiants en ingénierie.
Note de contenu :	Sommaire 1. Matrices and Systems of Linear Equations. Introduction to Matrices and Systems of Linear Equations. Echelon Form and Gauss-Jordan Elimination. Consistent Systems of Linear Equations. Applications. Matrix Operations. Algebraic Properties of Matrix Operations. Linear Independence and Nonsingular Matrices. Data Fitting, Numerical Integration, and Numerical Differentiation. Matrix Inverses and Their Properties. 2. The Vector Space R^n. Introduction. Vector Space Properties of R^n. Examples of Subspaces. Bases for Subspaces. Dimension. Orthogonal Bases for Subspaces. Linear Transformations from R^n to R^m. Least-Squares Solutions to Inconsistent Systems, with Applications to Data Fitting. Theory and Practice of Least Squares. 3. The Eigenvalue Problem. Introduction. Determinants and the Eigenvalue Problem. Elementary Operations and Determinants. Eigenvalues and the Characteristic Polynomial. Eigenvectors and Eigenspaces. Complex Eigenvalues and Eigenvectors. Similarity Transformations and Diagonalization. Difference Equations; Markov Chains; Systems of Differential Equations. 4. Vector Spaces and Linear Transformations. Introduction. Vector Spaces. Subspaces. Linear Independence, Bases, and Coordinates. Dimension. Inner Product Spaces, Orthogonal Bases, and Projections. Linear Transformations. Operations with Linear Transformations. Matrix Representations for Linear Transformations. Change of Basis and Diagonalization. 5. Determinants. Introduction. Cofactor Expansions of Determinants. Cramer's Rule. Applications of Determinants: Inverses and Wronksians. 6. Eigenvalues and Applications. Quadratic Forms. Systems of Differential Equations. Transformation to Hessenberg Matrices. Eigenvalues of Hessenberg Matrices. Householder Transformations. The QR Factorization and Least-Squares Solutions. Matrix Polynomials and the Cayley-Hamilton Theorem. Generalized Eigenvectors and Solutions of Systems of Differential Equations. 7. Numerical methods in linear algebra 7.1 computer arithmetic and roundoff(optional) 7.2 Gaussian elimination 7.3 The power methode for eigenvalues 7.4 The inverse power methode for the eigenvalue problem 7.5 Reduction tohessenberg form 7.6 Esti igenvalues of hessenberg matrices Index
Côte titre :	Fs/14318

Introduction to linear algebra [texte imprimé] / Lee W. Johnson ; R. Dean Riess ; Jimmy T. Arnold  . -  3e éd. . - Reading, Mass. : Addison-Wesley, 1993 . - 1 v. (534 p.) : ill. (some col.) ; 25 cm.
ISBN : 978-0-201-56801-1
Includes index

Catégories :	Mathématique
Mots-clés :	Algèbre linéaire
Index. décimale :	512 Algèbre
Résumé :	Cet ouvrage met l'accent à la fois sur le calcul pratique et sur les principes théoriques et se concentre sur l'introduction précoce de la théorie des matrices et des systèmes d'équations linéaires, des concepts élémentaires vectoriels-espace et du problème des valeurs propres. Avec une augmentation progressive du niveau de difficulté, un style d'écriture accessible et l'intégration de MATLAB, ce texte est une excellente introduction pour les étudiants en ingénierie.
Note de contenu :	Sommaire 1. Matrices and Systems of Linear Equations. Introduction to Matrices and Systems of Linear Equations. Echelon Form and Gauss-Jordan Elimination. Consistent Systems of Linear Equations. Applications. Matrix Operations. Algebraic Properties of Matrix Operations. Linear Independence and Nonsingular Matrices. Data Fitting, Numerical Integration, and Numerical Differentiation. Matrix Inverses and Their Properties. 2. The Vector Space R^n. Introduction. Vector Space Properties of R^n. Examples of Subspaces. Bases for Subspaces. Dimension. Orthogonal Bases for Subspaces. Linear Transformations from R^n to R^m. Least-Squares Solutions to Inconsistent Systems, with Applications to Data Fitting. Theory and Practice of Least Squares. 3. The Eigenvalue Problem. Introduction. Determinants and the Eigenvalue Problem. Elementary Operations and Determinants. Eigenvalues and the Characteristic Polynomial. Eigenvectors and Eigenspaces. Complex Eigenvalues and Eigenvectors. Similarity Transformations and Diagonalization. Difference Equations; Markov Chains; Systems of Differential Equations. 4. Vector Spaces and Linear Transformations. Introduction. Vector Spaces. Subspaces. Linear Independence, Bases, and Coordinates. Dimension. Inner Product Spaces, Orthogonal Bases, and Projections. Linear Transformations. Operations with Linear Transformations. Matrix Representations for Linear Transformations. Change of Basis and Diagonalization. 5. Determinants. Introduction. Cofactor Expansions of Determinants. Cramer's Rule. Applications of Determinants: Inverses and Wronksians. 6. Eigenvalues and Applications. Quadratic Forms. Systems of Differential Equations. Transformation to Hessenberg Matrices. Eigenvalues of Hessenberg Matrices. Householder Transformations. The QR Factorization and Least-Squares Solutions. Matrix Polynomials and the Cayley-Hamilton Theorem. Generalized Eigenvectors and Solutions of Systems of Differential Equations. 7. Numerical methods in linear algebra 7.1 computer arithmetic and roundoff(optional) 7.2 Gaussian elimination 7.3 The power methode for eigenvalues 7.4 The inverse power methode for the eigenvalue problem 7.5 Reduction tohessenberg form 7.6 Esti igenvalues of hessenberg matrices Index
Côte titre :	Fs/14318