Vectors and Matrices
Published on 9. May 2014
192 pages
978-1-4832-8043-1 (ISBN)
Description
Vectors and Matrices provides a progressive approach to vectors and matrices. The first half of this book is devoted to geometry, introducing matrices through its association with geometry mappings, while the rest of the chapters focus on the importance of matrices in non-geometric situations, such as the theory of linear equations and eigenvector theory. The power of eigenvector theory and its application to some problems in biology, probability, and genetics are also reviewed. Other topics include the product of scalar and vector, vector equation of a line, linear dependence, three-dimensional mappings, and orthogonal matrices. The transpose of a matrix and vector, rectangular matrices, inverse of a square matrix, and eigenvectors of a matrix are likewise emphasized in this text. This publication is beneficial to students and researchers conducting work on vectors and matrices.
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Pamela Liebeck
Vectors and Matrices
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10/1971
Pergamon
€24.76
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Content
Preface1 Vectors and Sealars Introduction Types of Numbers Properties of Numbers Exercise 1a Vectors Addition of Vectors Product of Scalar and Vector Summary Exercise 1b2 The Inner Product Introduction Inner Product Exercise 2a Position Vectors The Vector Equation of a Line The Distributive Property of Inner Product Summary Exercise 2b3 Vectors in Three Dimensions Introduction Three-Dimensional Coordinate Vectors The Vector Product Points, Lines and Planes Exercise 3a The Equations of a Line The Equation of a Plane-Linear Dependence Summary Exercise 3b4 Geometry Mappings Introduction Geometry Mappings Product of Mappings Exercise 4a Linear Mappings Matrices Three-Dimensional Mappings Summary Exercise 4b5 Classification of Two by Two Matrices Introduction Area and Determinants Isometric Mappings and Orthogonal Matrices Many-One Mappings and Singular Matrices Inverse Mappings and Inverse Matrices Exercise 5a Product of Mappings and Product of Matrices Transpose of a Matrix and Transpose of a Vector Summary Exercise 5b6 Classification of Three by Three Matrices Introduction Volume and Determinants Isometric Mappings and Orthogonal Matrices Many-One Mappings and Singular Matrices Inverse Mappings and Inverse Matrices Exercise 6a Product of Mappings and Product of Matrices Transpose of a Matrix and Transpose of a Vector Summary Exercise 6b7 Generalized Vectors and Matrices Introduction n-Dimensional Vectors Polynomials as Vectors Age Distribution Vectors Exercise 7a Rectangular Matrices Incidence Matrices Dominance Matrices Summary Exercise 7b8 Linear Equations Introduction Elementary Row Operations Inverse of a Square Matrix Exercise 8a Consistent and Inconsistent Equations The Echelon Form Calculating Aids Summary Exercise 8b9 Eigenvectors Introduction Eigenvectors of a Matrix The Characteristic Equation Exercise 9a Diagonalization Symmetric Matrices Summary Exercise 9b10 Some Applications of Eigenvectors Introduction Quadratic Forms Exercise 10a Recurring Processes Probability Summary Outlook Exercise 10bBibliographyAnswers to the ExercisesIndex
