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This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software. Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.

Algebra --- algebra --- lineaire algebra --- Algebra. --- Algebras, Linear. --- Matrix theory. --- Àlgebra lineal --- Matrius (Matemàtica)

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"The thoroughly revised and updated second edition of this acclaimed text has several new and expanded sections and more than 1,100 exercises"--

Algebra --- Matrices --- Matrices. --- Mathematics --- Physical Sciences & Mathematics --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Matrius (Matemàtica) --- Àlgebra de matrius --- Àlgebra matricial --- Càlcul de matrius --- Càlcul matricial --- Matrius (Àlgebra) --- Àlgebra abstracta --- Àlgebra universal

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Anàlisi multivariable --- Anàlisi multivariant --- Estadística matemàtica --- Matrius (Matemàtica) --- Anàlisi de conglomerats --- Anàlisi de correspondències (Estadística) --- Anàlisi discriminant --- Modelització multiescala --- Models d'equacions estructurals --- Anàlisi conjunt (Màrqueting) --- Multivariate analysis. --- Multivariate distributions --- Multivariate statistical analysis --- Statistical analysis, Multivariate --- Analysis of variance --- Mathematical statistics --- Matrices

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This book presents a general method for deriving higher-order statistics of multivariate distributions with simple algorithms that allow for actual calculations. Multivariate nonlinear statistical models require the study of higher-order moments and cumulants. The main tool used for the definitions is the tensor derivative, leading to several useful expressions concerning Hermite polynomials, moments, cumulants, skewness, and kurtosis. A general test of multivariate skewness and kurtosis is obtained from this treatment. Exercises are provided for each chapter to help the readers understand the methods. Lastly, the book includes a comprehensive list of references, equipping readers to explore further on their own.

Anàlisi multivariable --- Anàlisi multivariant --- Estadística matemàtica --- Matrius (Matemàtica) --- Anàlisi de conglomerats --- Anàlisi de correspondències (Estadística) --- Anàlisi discriminant --- Modelització multiescala --- Models d'equacions estructurals --- Anàlisi conjunt (Màrqueting) --- Multivariate analysis. --- Multivariate distributions --- Multivariate statistical analysis --- Statistical analysis, Multivariate --- Analysis of variance --- Mathematical statistics --- Matrices --- Statistics. --- Statistical Theory and Methods. --- Statistics and Computing. --- Data processing. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics

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Àlgebra abstracta --- Àlgebres de Jordan --- Àlgebres de Lie --- Àlgebres no associatives --- Matrius (Matemàtica) --- Teoria dels reticles --- Lògica matemàtica --- Algebra, Abstract. --- Logic, Symbolic and mathematical. --- Abstract algebra --- Algebra, Universal --- Logic, Symbolic and mathematical --- Set theory --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Syllogism