## Matrix Theory and Applications with MATLABDesigned for use in a second course on linear algebra, Matrix Theory and Applications with MATLAB covers the basics of the subject-from a review of matrix algebra through vector spaces to matrix calculus and unitary similarity-in a presentation that stresses insight, understanding, and applications. Among its most outstanding features is the integration of MATLAB throughout the text. Each chapter includes a MATLAB subsection that discusses the various commands used to do the computations in that section and offers code for the graphics and some algorithms used in the text. All of the material is presented from a matrix point of view with enough rigor for students to learn to compose arguments and proofs and adjust the material to cover other problems. The treatment includes optional subsections covering applications, and the final chapters move beyond basic matrix theory to discuss more advanced topics, such as decompositions, positive definite matrices, graphics, and topology. Filled with illustrations, examples, and exercises that reinforce understanding, Matrix Theory and Applications with MATLAB allows readers to experiment and visualize results in a way that no other text does. Its rigor, use of MATLAB, and focus on applications better prepares them to use the material in their future work and research, to extend the material, and perhaps obtain new results of their own. |

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### Contents

Review of Matrix Algebra | 1 |

Introduction to Vector Spaces | 29 |

Similarity | 75 |

Matrix Calculus | 117 |

Normed Vector Spaces | 157 |

Unitary Similarity | 205 |

Singular Value Decomposition | 235 |

LU and QR Decompositions | 265 |

Properties of Eigenvalues and Eigenvectors | 291 |

Hermitian and Positive Definite Matrices | 309 |

Graphics and Topology | 331 |

MATLAB | 347 |

367 | |

### Common terms and phrases

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