当前位置:
X-MOL 学术
›
Linear Multilinear Algebra
›
论文详情
Our official English website, www.x-mol.net, welcomes your
feedback! (Note: you will need to create a separate account there.)
Simple proof of existence of a complex eigenvalue of a complex square matrix …and yet another proof of the fundamental theorem of algebra with linear algebra
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2021-04-13 , DOI: 10.1080/03081087.2021.1913981 Luis T. Magalhães 1
中文翻译:
复方阵复特征值存在的简单证明……以及代数基本定理与线性代数的另一个证明
更新日期:2021-04-13
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2021-04-13 , DOI: 10.1080/03081087.2021.1913981 Luis T. Magalhães 1
Affiliation
We give a simple proof of the existence of a complex eigenvalue of real or complex square matrices with Linear Algebra accessible to students beginning a first course on the subject, namely using just the Cauchy–Schwarz inequality in , linear independence and the matrix product, together with the Weierstrass extreme value theorem. It yields an equally simple proof of the Fundamental Theorem of Algebra with Linear Algebra.
中文翻译:
复方阵复特征值存在的简单证明……以及代数基本定理与线性代数的另一个证明
我们给出了一个简单的证明,证明了实数或复数方阵的复数特征值的存在,学生可以使用线性代数开始关于该主题的第一门课程,即仅使用 Cauchy-Schwarz 不等式,线性独立性和矩阵乘积,以及 Weierstrass 极值定理。它用线性代数产生了代数基本定理的同样简单的证明。