An $n \times n$ matrix is said to be totally nonnegative if every minor of $A$ is nonnegative. In this paper we completely characterize all possible Jordan canonical forms of irreducible totally nonnegative matrices. Our approach is mostly combinatorial and is based on the study of weighted planar diagrams associated with totally nonnegative matrices.

Keywords:

totally nonnegative matrices, planar diagrams, principal rank, Jordan canonical form totally nonnegative matrices, planar diagrams, principal rank, Jordan canonical form

MSC Classifications:

15A21, 15A48, 05C38 show english descriptions Canonical forms, reductions, classification
Positive matrices and their generalizations; cones of matrices
Paths and cycles [See also 90B10] 15A21 - Canonical forms, reductions, classification
15A48 - Positive matrices and their generalizations; cones of matrices
05C38 - Paths and cycles [See also 90B10]

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