@article {MATHEDUC.06271811,
author = {Van Schaftingen, Jean},
title = {A direct proof of the existence of eigenvalues and eigenvectors by Weierstrass's theorem.},
year = {2013},
journal = {American Mathematical Monthly},
volume = {120},
number = {8},
issn = {0002-9890},
pages = {741-746},
publisher = {Mathematical Association of America (MAA), Washington, DC},
doi = {10.4169/amer.math.monthly.120.08.741},
abstract = {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)},
msc2010 = {H65xx},
identifier = {2014d.00691},
}