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A Direct Proof of the Existence of Eigenvalues and Eigenvectors by Weierstrass’s Theorem

Jean Van Schaftingen
The American Mathematical Monthly
Vol. 120, No. 8 (October 2013), pp. 741-746
DOI: 10.4169/amer.math.monthly.120.08.741
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.120.08.741
Page Count: 6
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A Direct Proof of the Existence of Eigenvalues and Eigenvectors by Weierstrass’s Theorem
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Abstract

Abstract 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.

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