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Eigenvalues and eigenvectors for matrices over distributive lattices. (English) Zbl 0932.15005
This paper obtains the basic properties of eigenvectors and eigenvalues of finite matrices over complete distributive lattices.

MSC:
15A18 Eigenvalues, singular values, and eigenvectors
15B33 Matrices over special rings (quaternions, finite fields, etc.)
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
06D05 Structure and representation theory of distributive lattices
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References:
[1] Birkhoff, G., Lattice theory, (1967), Amer. Math. Soc Providence, RI · Zbl 0126.03801
[2] Rutherford, D.E., The eigenvalue problem for Boolean matrices, (), 25-38 · Zbl 0132.26403
[3] Blyth, T.S., On eigenvectors of Boolean matrices, (), 196-204 · Zbl 0151.01802
[4] Kirkland, S.; Pullman, N.J., Boolean spectral theory, Linear algebra appl., 175, 177-190, (1992) · Zbl 0769.15007
[5] Cechlarova, K., Eigenvectors in bottleneck algebra, Linear algebra appl., 175, 63-67, (1992) · Zbl 0756.15014
[6] Zhao, C.K., On matrix equations in a class of complete and completely distributive lattices, Fuzzy sets and systems, 22, 303-320, (1987) · Zbl 0621.06006
[7] Zhang, K.L., Determinant theory for D_{01}-lattice matrices, Fuzzy sets and systems, 62, 347-353, (1994) · Zbl 0836.15002
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