Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/19862
Title: The E-eigenvectors of tensors
Authors: Hu, S
Qi, L 
Keywords: E-characteristic polynomial
E-eigenvector
Invariants
Nonsingular
Tensor
Issue Date: 2013
Publisher: Taylor & Francis
Source: Linear and multilinear algebra, 2013, v. 62, no. 10, p. 1388-1402 How to cite?
Journal: Linear and multilinear algebra 
Abstract: We first show that the eigenvector of a tensor is well defined. The differences between the eigenvectors of a tensor and its E-eigenvectors are the eigenvectors on the nonsingular projective variety (Formula presented.). We show that a generic tensor has no eigenvectors on (Formula presented.). Actually, we show that a generic tensor has no eigenvectors on a proper nonsingular projective variety in (Formula presented.). By these facts, we show that the coefficients of the E-characteristic polynomial are algebraically dependent. Actually, a certain power of the determinant of the tensor can be expressed through the coefficients besides the constant term. Hence, a nonsingular tensor always has an E-eigenvector. When a tensor (Formula presented.) is nonsingular and symmetric, its E-eigenvectors are exactly the singular points of a class of hypersurfaces defined by (Formula presented.) and a parameter. We give explicit factorization of the discriminant of this class of hypersurfaces which completes Cartwright and Strumfels¡¦ formula. We show that the factorization contains the determinant and the E-characteristic polynomial of the tensor (Formula presented.) as irreducible factors.
URI: http://hdl.handle.net/10397/19862
ISSN: 0308-1087
EISSN: 1563-5139
DOI: 10.1080/03081087.2013.828721
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