## Linear Algebra: Concepts and MethodsAny student of linear algebra will welcome this textbook, which provides a thorough treatment of this key topic. Blending practice and theory, the book enables the reader to learn and comprehend the standard methods, with an emphasis on understanding how they actually work. At every stage, the authors are careful to ensure that the discussion is no more complicated or abstract than it needs to be, and focuses on the fundamental topics. The book is ideal as a course text or for self-study. Instructors can draw on the many examples and exercises to supplement their own assignments. End-of-chapter sections summarize the material to help students consolidate their learning as they progress through the book. |

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#### LibraryThing Review

User Review - amarcobio - LibraryThingVery good introduction to linear algebra. It has a somewhat abstract/formak approach, in which all concepts and methods are developed from a reduced set of axions, a few definitions, ans a large ... Read full review

### Contents

before we begin | 1 |

1 Matrices and vectors | 10 |

2 Systems of linear equations | 59 |

3 Matrix inversion and determinants | 90 |

4 Rank range and linear equations | 131 |

5 Vector spaces | 149 |

6 Linear independence bases and dimension | 172 |

7 Linear transformations and change of basis | 210 |

8 Diagonalisation | 247 |

### Common terms and phrases

Activity addition and scalar algebra augmented matrix basis of Rn basis vectors calculations Cartesian equation coefficient cofactor expansion complex numbers corresponding eigenvectors deﬁne deﬁnition denote determinant diagonal matrix eigenspace eigenvalues eigenvector corresponding eigenvectors elementary matrix entries equal equations Ax Example expressed ﬁnd ﬁrst given Hermitian homogeneous system idempotent integer intersection invertible matrix linear combination linear equations linear span linear system linear transformation linearly independent non-zero null space obtain ofthe orthogonal diagonalisation orthogonal matrix orthonormal basis plane in R3 position vector positive definite Problem Proof properties prove PTAP quadratic form real numbers reduced row echelon row echelon form row operations row space satisfy scalar multiplication set of vectors solve standard coordinates subset subspace Suppose symmetric matrix system Ax system of equations system of linear transition matrix vector equation vector space vectors v1 write xTAx zero vector