
06271811
j
2014d.00691
Van Schaftingen, Jean
A direct proof of the existence of eigenvalues and eigenvectors by Weierstrass's theorem.
Am. Math. Mon. 120, No. 8, 741746 (2013).
2013
Mathematical Association of America (MAA), Washington, DC
EN
H65
eigenvector
eigenvalue
linear operator
Weierstrass theorem
polynomialfree proof
Zbl 1175.30009
doi:10.4169/amer.math.monthly.120.08.741
arxiv:1109.6821
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 polynomialfree 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, 6768 (2009; Zbl 1175.30009)]).
Tin Yau Tam (Auburn)