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On nonnegative
matrices
Mordechai Lewin |
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Vol. 36 (1971), No. 3, 753–759
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Abstract |
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The following characterisation of totally indecomposable nonnegative n-square matrices is introduced: A nonnegative n-square matrix is totally indecomposable if and only if it diminishes the number of zeros of every n-dimensional nonnegative vector which is neither positive nor zero. From this characterisation it follows quite easily that: I. The class of totally indecomposable nonnegative n-square matrices is closed with respect to matrix multiplication. II. The (n − 1)-st power of a matrix of that class is positive. A very short proof of two equivalent versions of the König-Frobenius duality theorem on (0,1)-matrices is supplied at the end. |
Mathematical Subject Classification
Primary: 15.60
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Milestones
Received: 27 January 1970
Published: 1 March 1971
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Authors |
| Mordechai Lewin | |
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