Combinatorial Bases, Derived Jordan Sets and the Equality of the Height and Level Characteristics of an M-Matrix
نویسنده
چکیده
We continue our series of papers on the graph theoretic spectral theory of matrices. Let A be an Mmatrix. We introduce the concepts of combinatorial vectors and proper combinatorial vectors in the generalized nuUspacc E(A) of A. \\e explore the properties of combinatorial bases for E(A) and Jordan bases for E(A) derived from proper combinatorial sets of vectors. We use properties of these bases to prove additional new conditions for the equality of the (spectral) height (or Weyr) characteristic and the (graph theoretic) level characteristic of A. "We also explore the role of the HaU Marriage Condition, weU structured graphs and their anchored chain decompositions in the study of the equality of the two characteristics.
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