## Matrices and Linear Transformations"Comprehensive . . . an excellent introduction to the subject." — Electronic Engineer's Design Magazine.This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. The first seven chapters, which require only a first course in calculus and analytic geometry, deal with matrices and linear systems, vector spaces, determinants, linear transformations, similarity, polynomials, and polynomial matrices. Chapters 8 and 9, parts of which require the student to have completed the normal course sequence in calculus and differential equations, provide introductions to matrix analysis and numerical linear algebra, respectively. Among the key features are coverage of spectral decomposition, the Jordan canonical form, the solution of the matrix equation AX = XB, and over 375 problems, many with answers. |

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Unlike Elementary Matrix Theory, by Howard Eves, this book does share a lot of material with the linear algebra texts published in 2010. However, there is still some material in this book, such as canonical forms, that doesn't typically appear in introductory linear algebra books. While the author does write clearly, the writing is at a more mathematically sophisticated level than the books aimed at introducing linear algebra to students in 2010. Considering the very cheap price of this Dover reprint, this is a worthwhile second book to have on linear algebra. See also Elementary Matrix Theory, by Howard Eves, to find a book with much material that is difficult to find in more recently published books.

### Contents

Matrices and Linear Systems | 1 |

Vector Spaces | 67 |

Determinants | 104 |

Linear Transformations | 124 |

Part I | 178 |

Polynomials and Polynomial Matrices | 215 |

Part II | 236 |

Matrix Analysis | 255 |

Numerical Methods | 272 |

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### Common terms and phrases

A(xi algebraic B(xi c(xi c(xl characteristic polynomial characteristic value compute Consider converges corollary Crd^al d(xi defined Definition det(x determined diagonal matrix echelon form elementary matrices elementary row operations elements equation Example Exercise exists f(Ai f(xi field follows from Theorem form a basis function hence Hermitian Hermitian matrix independent characteristic vectors integers inverse isomorphic Jordan blocks Jordan canonical form Jordan canonical matrix linear operator linear transformation linearly independent ll(x lower triangular m x n matrix m(xl minimum polynomial monic Mtx^tl n x n nilpotent nonsingular matrix nonzero rows one-to-one orthogonal matrix orthonormal basis p(Ai p(xi p(xl partitioned Proof Let proof of Theorem properties Prove Theorem q(xi r(xl rank reader real numbers result row equivalent row-reduced echelon satisfies Section sequence set of vectors Show solution solved Span subset subspace symmetric system AX t-invariant t(al triangular matrix unique unitary matrix vector space zero