Complex eigenvalues before the Fundamental Theorem of Algebra |
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| Authors: | Armando Machado |
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| Affiliation: | 1. Faculty of Sciences of the University of Lisbon, Department of Mathematics , Campo Grande, Lisboa, Portugal armac@ptmat.fc.ul.pt |
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| Abstract: | We present an elementary proof of the existence of an eigenvalue for an endomorphism of a complex vector space and we derive the Fundamental Theorem of Algebra as a corollary of this existence. We also present new proofs for the corresponding results for endomorphisms of real vector spaces. |
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| Keywords: | complex eigenvalues fundamental theorem of algebra invariant vector subspaces |
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