A Direct Proof of the Existence of Eigenvalues and Eigenvectors by Weierstrass's Theorem
Jean Van Schaftingen · American Mathematical Monthly · 2013
The existence of an eigenvector and an eigenvalue of a linear operator on a complex vector space is proved in the spirit of Argand's proof of the fundamental theorem of algebra. The proof relies only on Weierstrass's theorem, the definition of the inverse of a linear operator, and algebraic identities.