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<p><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">第1章 线性空间与线性算子</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">§1．1 集合及其运算</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">一、集合的概念</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">二、集合的包含关系与子集</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">三、集合的交、并、差运算</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">四、集合的直积</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">五、n个集合的交、并及直积</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">§1．2 映射及其性质</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">一、映射的概念</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">二、几种重要的映射</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">三、逆映射与复合映射</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">四、可数集及其性质</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">五、任意多个集合的交、并运算</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">六、数域，实数集的确界，重要不等式</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">§1．3 线性空间</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">一、线性空间的概念</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">二、线性空间的子空间</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">§1．4 线性空间的基与维数</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">一、集合的线性相关性</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">二、基与维数</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">三、元素在基下的坐标</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">§1．5 线性算子</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">一、线性算子及其性质</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">二、线性算子的零空间</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">三、线性算子的运算</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">四、线性算子的矩阵</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">习题1</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">A</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">B</span><br/><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">第2章 矩阵的相似标准形</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">§2．1 方阵的特征值与特征向量</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">一、特征值与特征向量的概念</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">二、有关特征值与特征向量的重要结论</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">§2．2 相似矩阵</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">一、相似矩阵及其性质</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">二、方阵的相似对角形</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">§2．3 多项式矩阵及其Smith标准形</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">一、多项式的有关概念</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">二、多项式矩阵</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">三、多项式矩阵的初等变换</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">四、多项式矩阵的Smith标准形</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">§2．4 多项式矩阵的不变因子与初等因子</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">一、多项式矩阵的行列式因子与不变因子</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">二、多项式矩阵的初等因子</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">三、多项式矩阵等价的充要条件</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">§2．5 矩阵的Jordan标准形和有理标准形</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">一、方阵相似的充要条件</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">二、方阵的Jordan标准形</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">三、方阵的有理标准形</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">§2．6 方阵的零化多项式与最小多项式</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">一、方阵的零化多项式</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">……</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">第3章 赋范空间</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">第4章 矩阵分析</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">第5章 内积空间与Hermite矩阵</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">第6章 线性方程组的解法</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">第7章 插值法与数值逼近</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">第8章 数值积分与数值微分</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">第9章 常微分方程的数值解法</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">第10章 广义逆矩阵及其应用</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">参考文献</span><br/><span style="color: rgb(102, 102, 102); font-family: tahoma, arial, "Microsoft YaHei", "Hiragino Sans GB", u5b8bu4f53, sans-serif; font-size: 14px; background-color: rgb(255, 255, 255);">A类习题参考答案</span></p>
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