## Introduction to Matrices and VectorsRealizing that matrices can be a confusing topic for the beginner, the author of this undergraduate text has made things as clear as possible by focusing on problem solving, rather than elaborate proofs. He begins with the basics, offering students a solid foundation for the later chapters on using special matrices to solve problems. The first three chapters present the basics of matrices, including addition, multiplication, and division, and give solid practice in the areas of matrix manipulation where the laws of algebra do not apply. In later chapters the author introduces vectors and shows how to use vectors and matrices to solve systems of linear equations. He also covers special matrices — including complex numbers, quaternion matrices, and matrices with complex entries — and transpose matrices; the trace of a matrix; the cross product of matrices; eigenvalues and eigenvectors; and infinite series of matrices. Exercises at the end of each section give students further practice in problem solving. Prerequisites include a background in algebra, and in the later chapters, a knowledge of solid geometry. The book was designed as an introductory text for college freshmen and sophomores, but selected chapters can also be used to supplement advanced high school classes. Professionals who need a better understanding or review of the subject will also benefit from this concise guide. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

DEFINITION EQUALITY AND ADDITION OF MATRICES | 1 |

MULTIPLICATION OF MATRICES | 25 |

DIVISION OF MATRICES | 56 |

VECTORS AND LINEAR EQUATIONS | 81 |

SPECIAL MATRICES OF PARTICULAR INTEREST | 118 |

MORE ALGEBRA OF MATRICES AND VECTORS | 126 |

EIGENVALUES AND EIGENVECTORS | 147 |

INFINITE SERIES OF MATRICES | 152 |

### Other editions - View all

### Common terms and phrases

addition and subtraction Addition of Matrices atomic physics Available in U.S. cap product Chapter circle product commutative law complex numbers compute coordinates corresponding entry cross product defined DEFINITION Let different from zero directed line segment directed segment PQ eigenvalue entry zero expression following theorem formula geometric theorems Hence illustrations inequality ith row j'th jth column law of exponents least equation satisfied length linear equations mathematical induction mathematics matrix algebra Matrix Multiplication Multiplication of Matrices n x n matrix notation ordinary algebra photographs plane polynomial equation PQ and PR preceding section proof proves the following real numbers reciprocal matrix represents the vector row and jth Show simply skew matrix solution Solve the equation square root Suppose system of equations terms in unknowns THEOREM Let theorem of Section THEORY three-dimensional space tion U A V unit matrix vector algebra write zero matrix