## Linear Algebra and GeometryHong Kong University Press, 1974年1月1日 - 320 頁 Linear algebra is now included in the undergraduate curriculum of most universities. It is generally recognized that this branch of algebra, being less abstract and directly motivated by geometry, is easier to understand than some other branches and that because of the wide applications it should be taught as soon as possible. This book is an extension of the lecture notes for a course in algebra and geometry for first-year undergraduates of mathematics and physical sciences. Except for some rudimentary knowledge in the language of set theory the prerequisites for using the main part of the book do not go beyond form VI level. Since it is intended for use by beginners, much care is taken to explain new theories by building up from intuitive ideas and by many illustrative examples, though the general level of presentation is thoroughly axiomatic. Another feature of the book for the more capable students is the introduction of the language and ideas of category theory through which a deeper understanding of linear algebra can be achieved. |

### 內容

1 | |

45 | |

Ch III AFFINE GEOMETRY | 96 |

Ch IV PROJECTIVE GEOMETRY | 118 |

Ch V MATRICES | 155 |

Ch VI MULTILINEAR FORMS | 196 |

Ch VII EIGENVALUES | 230 |

Ch VIII INNER PRODUCT SPACES | 267 |

Index | 306 |

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### 常見字詞

addition affine space affine transformation algebraic automorphism bilinear form called Clearly column composition condition Consequently consider consisting Conversely coordinates correspondence defined definition denote dependent determinant dimension direct distinct dual eigenvalues elementary elements endomorphism equal equations equivalent euclidean space example exists Find finite finite-dimensional linear space fixed formation function functor geometry given hence holds identity inner product intersection invariant inverse isomorphism linear combination linear space linear transformation linear variety linearly independent mapping means morphisms n-dimensional non-zero vector objects obtain orthogonal orthonormal base pair plane points polynomial positive projective projective space PROOF properties Prove real linear space real number relative respectively result satisfies scalar self-adjoint Show Similarly space X subset subspace theorem theory trans unique unitary space write zero