| 开本：16开 |
| 纸张：轻型纸 |
| 包装：平装-胶订 |
| 是否套装：否 |
| 国际标准书号ISBN：9787121501258 |
| 所属分类：图书>自然科学>数学>代数数论组合理论 |
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章 行列式 节 阶与 阶行列式··································································· 一、 阶行列式 ············································································· 二、 阶行列式 ············································································· 节 级排列与对换······································································ 一、 级排列 ················································································ 二、对换 ····················································································· 三节 阶行列式 ············································································ 一、 阶行列式定义······································································· 二、几种特殊的行列式 ··································································· 四节 行列式的质及其应用 ···························································· 一、行列式的质 ······································································ 二、行列式质的应用 ································································ 五节 行列式按行（列）展开 ···························································· 一、行列式的展开 ······································································ 二、行列式展开的应用 ································································ 六节 克拉默法则及其应用 ······························································· 一、克拉默法则 ········································································· 二、克拉默法则的应用 ································································ 七节 应用实例―电路网络问题 ······················································ 数学家阅读小知识··············································································· 复················································································· 章 矩阵 节 矩阵的概念 ··········································································· 一、矩阵概念的引入 ··································································· 二、几种特殊的矩阵 ··································································· 节 矩阵的运算 ··········································································· 一、矩阵的加减法 ······································································ 二、数与矩阵的乘法 ··································································· 三、矩阵的乘法 ········································································· 四、矩阵的转置 ········································································· 五、方阵的行列式 ······································································ 六、伴随矩阵 ············································································节 矩阵的逆··············································································· 一、逆矩阵的概念和质 ····························································· 二、矩阵可逆的条件 ··································································· 四节 分块矩阵··············································································· 一、分块矩阵的概念 ··································································· 二、分块矩阵的运算 ··································································· 五节 矩阵的初等变换 ····································································· 一、矩阵初等变换的概念和质 ···················································· 二、初等矩阵及初等变换 ····························································· 三、利用初等变换求矩阵的逆 ······················································· 六节 矩阵的秩··············································································· 一、矩阵秩的概念 ······································································ 二、矩阵秩的质 ······································································ 七节 应用案例―希尔密码（ ） ········································ 数学家阅读小知识··············································································· 复·················································································· 章 向量与向量空间 节 维向量及其线运算····························································· 一、 维向量 ············································································· 二、向量的运算 ·········································································单元 节 向量组的线相关 ······························································· 一、向量组线相关 ································································ 二、向量组线相关的质 ······················································· 三节 极大线无关组 ····································································· 一、极大线无关组的概念 ·························································· 二、求极大线无关组 ································································、向量组的等······································································ 四节 向量组的秩及其与矩阵秩的关系 ············································· 一、向量组的秩 ········································································· 二、向量组的秩与矩阵的秩的关系 ················································· 五节 向量空间············································································ 一、向量空间及子空间 ································································ 二、 维向量空间 的基变换 ······················································ 六节 向量的内积与正交向量组 ······················································ 一、 维向量的内积···································································· 二、正交向量组 ········································································· 七节 应用实例―混凝土配方 ······················································ 数学家阅读小知识············································································ 复·············································································· 章 线方程组 节 线方程组解的存在及判定 ················································ 一、齐次线方程组解的存在及判定 ··········································· 二、非齐次线方程组解的存在及判定 ········································ 节 齐次线方程组及其基础解系 ················································ 一、齐次线方程组解的结构 ······················································· 二、齐次线方程组的基础解系和通解 ··········································· 三节 非齐次线方程组的通解 ······················································ 四节 应用实例―食物配方 ························································· 数学家阅读小知识············································································ 复·············································································· 章 特征值与特征向量 节 特征值与特征向量的概念及质 ············································· 一、特征值与特征向量的概念 ······················································· 二、特征值和特征向量的质 ······················································· 节 相似矩阵············································································ 一、相似矩阵的概念和质 ·························································· 二、矩阵的对角化 ······································································ 三节 实对称矩阵及其对角化 ························································· 一、实对称矩阵的特征值与特征向量的质 ····································· 二、实对称矩阵的对角化 ····························································· 四节 应用实例············································································ 数学家阅读小知识············································································ 复·············································································· 章 二次型 节 二次型及其标准形 ······························································· 一、二次型的概念 ······································································ 二、二次型的矩阵 ······································································ 三、线变换与矩阵的合同 ·························································· 节 化二次型为标准形 ······························································· 一、正交变换法 ········································································· 二、拉格朗日配方法 ··································································· 三、初等变换法 ·········································································节 正定二次型 ········································································ 四节 应用实例―条件优化问题 ··················································· 数学家阅读小知识············································································ 复·············································································· 参考答案
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章 行列式 节 阶与 阶行列式··································································· 一、 阶行列式 ············································································· 二、 阶行列式 ············································································· 节 级排列与对换······································································ 一、 级排列 ················································································ 二、对换 ····················································································· 三节 阶行列式 ············································································ 一、 阶行列式定义······································································· 二、几种特殊的行列式 ··································································· 四节 行列式的质及其应用 ···························································· 一、行列式的质 ······································································ 二、行列式质的应用 ································································ 五节 行列式按行（列）展开 ···························································· 一、行列式的展开 ······································································ 二、行列式展开的应用 ································································ 六节 克拉默法则及其应用 ······························································· 一、克拉默法则 ········································································· 二、克拉默法则的应用 ································································ 七节 应用实例―电路网络问题 ······················································ 数学家阅读小知识··············································································· 复················································································· 章 矩阵 节 矩阵的概念 ··········································································· 一、矩阵概念的引入 ··································································· 二、几种特殊的矩阵 ··································································· 节 矩阵的运算 ··········································································· 一、矩阵的加减法 ······································································ 二、数与矩阵的乘法 ··································································· 三、矩阵的乘法 ········································································· 四、矩阵的转置 ········································································· 五、方阵的行列式 ······································································ 六、伴随矩阵 ············································································节 矩阵的逆··············································································· 一、逆矩阵的概念和质 ····························································· 二、矩阵可逆的条件 ··································································· 四节 分块矩阵··············································································· 一、分块矩阵的概念 ··································································· 二、分块矩阵的运算 ··································································· 五节 矩阵的初等变换 ····································································· 一、矩阵初等变换的概念和质 ···················································· 二、初等矩阵及初等变换 ····························································· 三、利用初等变换求矩阵的逆 ······················································· 六节 矩阵的秩··············································································· 一、矩阵秩的概念 ······································································ 二、矩阵秩的质 ······································································ 七节 应用案例―希尔密码（ ） ········································ 数学家阅读小知识··············································································· 复·················································································· 章 向量与向量空间 节 维向量及其线运算····························································· 一、 维向量 ············································································· 二、向量的运算 ·········································································单元 节 向量组的线相关 ······························································· 一、向量组线相关 ································································ 二、向量组线相关的质 ······················································· 三节 极大线无关组 ····································································· 一、极大线无关组的概念 ·························································· 二、求极大线无关组 ································································、向量组的等······································································ 四节 向量组的秩及其与矩阵秩的关系 ············································· 一、向量组的秩 ········································································· 二、向量组的秩与矩阵的秩的关系 ················································· 五节 向量空间············································································ 一、向量空间及子空间 ································································ 二、 维向量空间 的基变换 ······················································ 六节 向量的内积与正交向量组 ······················································ 一、 维向量的内积···································································· 二、正交向量组 ········································································· 七节 应用实例―混凝土配方 ······················································ 数学家阅读小知识············································································ 复·············································································· 章 线方程组 节 线方程组解的存在及判定 ················································ 一、齐次线方程组解的存在及判定 ··········································· 二、非齐次线方程组解的存在及判定 ········································ 节 齐次线方程组及其基础解系 ················································ 一、齐次线方程组解的结构 ······················································· 二、齐次线方程组的基础解系和通解 ··········································· 三节 非齐次线方程组的通解 ······················································ 四节 应用实例―食物配方 ························································· 数学家阅读小知识············································································ 复·············································································· 章 特征值与特征向量 节 特征值与特征向量的概念及质 ············································· 一、特征值与特征向量的概念 ······················································· 二、特征值和特征向量的质 ······················································· 节 相似矩阵············································································ 一、相似矩阵的概念和质 ·························································· 二、矩阵的对角化 ······································································ 三节 实对称矩阵及其对角化 ························································· 一、实对称矩阵的特征值与特征向量的质 ····································· 二、实对称矩阵的对角化 ····························································· 四节 应用实例············································································ 数学家阅读小知识············································································ 复·············································································· 章 二次型 节 二次型及其标准形 ······························································· 一、二次型的概念 ······································································ 二、二次型的矩阵 ······································································ 三、线变换与矩阵的合同 ·························································· 节 化二次型为标准形 ······························································· 一、正交变换法 ········································································· 二、拉格朗日配方法 ··································································· 三、初等变换法 ·········································································节 正定二次型 ········································································ 四节 应用实例―条件优化问题 ··················································· 数学家阅读小知识············································································ 复·············································································· 参考答案
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