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本套书以讲述线性空间和多项式环的结构及其态射为主线，遵循高等代数知识的内在规律和学生的认知规律安排内容体系，按照数学思维方式编写，着重培养数学思维能力。上册内容包括：线性方程组，行列式，n维向空间Kn，矩阵的运算，欧几里得空间Rn，矩阵的相抵、相似，以及矩阵的合同与二次型。下册内容包括：多项式环，线性空间，线性映射，具有度量的线性空间（欧几里得空间、酉空间、正交空间和辛空间），环、域和群的概念及重要例子，多重线性代数。 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