The study finds a condition for pseudo-diagonalization in max-plus matrices, suggesting their eigenvalues can be effectively calculated.
We provide a necessary and sufficient condition for matrices in the max-plus algebra to be pseudo-diagonalizable, calculate the powers of pseudo-diagonal matrices and prove the invariance of optimal-node matrices and separable matrices under similarity. As an application, we determine the eigenvalues and eigenspaces of pseudo-diagonalizable matrices.
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Zhang et al. (2025) studied this question.
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