A Direct Proof of the Existence of Eigenvalues and Eigenvectors by Weierstrass%26apos;s Theorem

作者:Van Schaftingen Jean*
来源:American Mathematical Monthly, 2013, 120(8): 741-746.
DOI:10.4169/amer.math.monthly.120.08.741

摘要

The existence of an eigenvector and an eigenvalue of a linear operator on a complex vector space is proved in the spirit of Argand%26apos;s proof of the fundamental theorem of algebra. The proof relies only on Weierstrass%26apos;s theorem, the definition of the inverse of a linear operator, and algebraic identities.

  • 出版日期2013-10