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 
have the same geometric multiplicity. We also prove that two-dimensional nonnegative tensors’ geometric multiplicity of eigenvalues is equal to algebraic multiplicity of eigenvalues.
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Li, Y., Yang, Q. & Yang, Y. A new definition of geometric multiplicity of eigenvalues of tensors and some results based on it. Front. Math. China 10, 1123–1146 (2015). https://doi.org/10.1007/s11464-015-0412-z
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DOI: https://doi.org/10.1007/s11464-015-0412-z