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)]).

Reviewer:

Tin Yau Tam (Auburn)