高等代数中用数学归纳法证明的类型
ypes of proofs by mathematical induction in advanced algebra
在数学证明中，数学归纳法是一种常见、重要的证明方法。这篇论文归纳总结了高等代数证明中适用数学归纳法的类型。这些类型包括：直接对正整数作归纳，对多项式的次数作归纳，对行列式的阶数作归纳，对方阵的阶数作归纳，对向量空间的维数作归纳。
In mathematical proofs, mathematical induction is a common and important proof method. This paper summarizes the types of proofs that are applicable to mathematical induction in advanced algebra. These types include: direct induction of positive integers, induction of the degree of polynomials, induction of the order of determinants, induction of the order of square matrices, and induction of the dimension of vector spaces.
吴晗
数学
数学归纳法多项式的次数行列式、方阵的阶数向量空间的维数
mathematical inductionthe degree of polynomialsthe order of determinants and square matricesthe dimensions of vector spaces
吴晗.高等代数中用数学归纳法证明的类型[EB/OL].(2024-10-18)[2025-08-18].https://chinaxiv.org/abs/202410.00122.点此复制
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