A new definition of geometric multiplicity of eigenvalues of tensors and some results based on it

Abstract

We give a new definition of geometric multiplicity of eigenvalues of tensors, and based on this, we study the geometric and algebraic multiplicity of irreducible tensors’ eigenvalues. We get the result that the eigenvalues with modulus ρ({A}) have the same geometric multiplicity. We also prove that twodimensional nonnegative tensors’ geometric multiplicity of eigenvalues is equal to algebraic multiplicity of eigenvalues.

Keywords

Irreducible tensor / Perron-Frobenius theorem / geometrically simple

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Higher Education Press and Springer-Verlag Berlin Heidelberg