\input zb-basic \input zb-matheduc \iteman{ZMATH 2014d.00691} \itemau{Van Schaftingen, Jean} \itemti{A direct proof of the existence of eigenvalues and eigenvectors by Weierstrass's theorem.} \itemso{Am. Math. Mon. 120, No. 8, 741-746 (2013).} \itemab The existence of an eigenvector and an eigenvalues of a linear operator on a complex vector space is proved. The proof relies only on Weierstrass' theorem (in the spirit of Argand's proof), the definition of the inverse of a linear operator, and algebraic identities. Eigenvalues and eigenvectors are defined without reference to polynomials so the author presents a polynomial-free proof of the existence of eigenvectors and eigenvalues. It is not the shortest proof (see [{\it A. R. Schep}, Am. Math. Mon. 116, No. 1, 67--68 (2009; Zbl 1175.30009)]). \itemrv{Tin Yau Tam (Auburn)} \itemcc{H65} \itemut{eigenvector; eigenvalue; linear operator; Weierstrass theorem; polynomial-free proof} \itemli{doi:10.4169/amer.math.monthly.120.08.741 arxiv:1109.6821} \end