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001484464 001__ 1484464
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001484464 019__ $$a1410757824
001484464 020__ $$a9783031395628$$q(electronic bk.)
001484464 020__ $$a303139562X$$q(electronic bk.)
001484464 020__ $$z3031395611
001484464 020__ $$z9783031395611
001484464 0247_ $$a10.1007/978-3-031-39562-8$$2doi
001484464 035__ $$aSP(OCoLC)1411307867
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001484464 049__ $$aISEA
001484464 050_4 $$aQA188$$b.F44 2024
001484464 08204 $$a512.5$$223/eng/20231208
001484464 1001_ $$aFeeman, Timothy G.,$$d1956-
001484464 24510 $$aApplied linear algebra and matrix methods /$$cTimothy G. Feeman.
001484464 264_1 $$aCham :$$bSpringer,$$c2024.
001484464 300__ $$a1 online resource (330 p.).
001484464 336__ $$atext$$btxt$$2rdacontent
001484464 337__ $$acomputer$$bc$$2rdamedia
001484464 338__ $$aonline resource$$bcr$$2rdacarrier
001484464 4901_ $$aSpringer Undergraduate Texts in Mathematics and Technology
001484464 5050_ $$aIntro -- Introduction -- Advice for Instructors -- Acknowledgments -- Contents -- 1 Vectors -- 1.1 Coordinates and Vectors -- 1.2 The Vector Norm -- 1.3 Angles and the Inner Product -- 1.4 Inner Product and Vector Arithmetic -- 1.5 Statistical Correlation -- 1.6 Information Retrieval -- 1.6.1 Comparing Movie Viewers -- 1.7 Distance on a Sphere -- 1.8 Bézier Curves -- 1.9 Orthogonal Vectors -- 1.10 Area of a Parallelogram -- 1.11 Projection and Reflection -- 1.12 The ``All-1s'' Vector -- 1.13 Exercises -- 1.14 Projects -- 2 Matrices -- 2.1 Matrices
001484464 5058_ $$a2.1.1 Algebraic Properties of Matrix Arithmetic -- 2.2 Matrix Multiplication -- 2.2.1 Algebraic Properties of Matrix Multiplication -- 2.3 The Identity Matrix, I -- 2.4 Matrix Inverses -- 2.5 Transpose of a Matrix -- 2.6 Exercises -- 3 Matrix Contexts -- 3.1 Digital Images -- 3.2 Information Retrieval Revisited -- 3.3 Markov Processes: A First Look -- 3.4 Graphs and Networks -- 3.5 Simple Linear Regression -- 3.6 k-Means -- 3.7 Projection and Reflection Revisited -- 3.8 Geometry of 22 Matrices -- 3.9 The Matrix Exponential -- 3.10 Exercises -- 3.11 Projects -- 4 Linear Systems
001484464 5058_ $$a4.1 Linear Equations -- 4.2 Systems of Linear Equations -- 4.3 Row Reduction -- 4.4 Row Echelon Forms -- 4.5 Matrix Inverses (And How to Find Them) -- 4.6 Leontief Input-Output Matrices -- 4.7 Cubic Splines -- 4.8 Solutions to AX=B -- 4.9 LU Decomposition -- 4.10 Affine Projections -- 4.10.1 Kaczmarz's Method -- 4.10.2 Fixed Point of an Affine Transformation -- 4.11 Exercises -- 4.12 Projects -- 5 Least Squares and Matrix Geometry -- 5.1 The Column Space of a Matrix -- 5.2 Least Squares: Projection into Col(A) -- 5.3 Least Squares: Two Applications -- 5.3.1 Multiple Linear Regression
001484464 5058_ $$a5.3.2 Curve Fitting with Least Squares -- 5.4 Four Fundamental Subspaces -- 5.4.1 Column-Row Factorization -- 5.5 Geometry of Transformations -- 5.6 Matrix Norms -- 5.7 Exercises -- 5.8 Project -- 6 Orthogonal Systems -- 6.1 Projections Revisited -- 6.2 Building Orthogonal Sets -- 6.3 QR Factorization -- 6.4 Least Squares with QR -- 6.5 Orthogonality and Matrix Norms -- 6.6 Exercises -- 6.7 Projects -- 7 Eigenvalues -- 7.1 Eigenvalues and Eigenvectors -- 7.2 Computing Eigenvalues -- 7.3 Computing Eigenvectors -- 7.4 Transformation of Eigenvalues -- 7.5 Eigenvalue Decomposition
001484464 5058_ $$a7.6 Population Models -- 7.7 Rotations of R3 -- 7.8 Existence of Eigenvalues -- 7.9 Exercises -- 8 Markov Processes -- 8.1 Stochastic Matrices -- 8.2 Stationary Distributions -- 8.3 The Power Method -- 8.4 Two-State Markov Processes -- 8.5 Ranking Web Pages -- 8.6 The Monte Carlo Method -- 8.7 Random Walks on Graphs -- 8.8 Exercises -- 8.9 Project -- 9 Symmetric Matrices -- 9.1 The Spectral Theorem -- 9.2 Norm of a Symmetric Matrix -- 9.3 Positive Semidefinite Matrices -- 9.3.1 Matrix Square Roots -- 9.4 Clusters in a Graph -- 9.5 Clustering a Graph with k-Means -- 9.6 Drawing a Graph
001484464 506__ $$aAccess limited to authorized users.
001484464 520__ $$aThis textbook is designed for a first course in linear algebra for undergraduate students from a wide range of quantitative and data driven fields. By focusing on applications and implementation, students will be prepared to go on to apply the power of linear algebra in their own discipline. With an ever-increasing need to understand and solve real problems, this text aims to provide a growing and diverse group of students with an applied linear algebra toolkit they can use to successfully grapple with the complex world and the challenging problems that lie ahead. Applications such as least squares problems, information retrieval, linear regression, Markov processes, finding connections in networks, and more, are introduced on a small scale as early as possible and then explored in more generality as projects. Additionally, the book draws on the geometry of vectors and matrices as the basis for the mathematics, with the concept of orthogonality taking center stage. Important matrix factorizations as well as the concepts of eigenvalues and eigenvectors emerge organically from the interplay between matrix computations and geometry. The R files are extra and freely available. They include basic code and templates for many of the in-text examples, most of the projects, and solutions to selected exercises. As much as possible, data sets and matrix entries are included in the files, thus reducing the amount of manual data entry required. .
001484464 650_6 $$aAlgèbre linéaire.
001484464 650_0 $$aAlgebras, Linear.$$0(DLC)sh 85003441
001484464 655_0 $$aElectronic books.
001484464 77608 $$iPrint version:$$aFeeman, Timothy G.$$tApplied Linear Algebra and Matrix Methods$$dCham : Springer International Publishing AG,c2024
001484464 830_0 $$aSpringer undergraduate texts in mathematics and technology.
001484464 852__ $$bebk
001484464 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-39562-8$$zOnline Access$$91397441.1
001484464 909CO $$ooai:library.usi.edu:1484464$$pGLOBAL_SET
001484464 980__ $$aBIB
001484464 980__ $$aEBOOK
001484464 982__ $$aEbook
001484464 983__ $$aOnline
001484464 994__ $$a92$$bISE