Abstract
Our purpose is to present a number of new facts about the structure of semipositive matrices, involving patterns, spectra and Jordon form, sums and products, and matrix equivalence, etc. Techniques used to obtain the results may be of independent interest. Examples include: any matrix with at least two columns is a sum, and any matrix with at least two rows, a product, of semipositive matrices. Any spectrum of a real matrix with at least 2 elements is the spectrum of a square semipositive matrix, and any real matrix, except for a negative scalar matrix, is similar to a semipositive matrix. M-matrices are generalized to the non-square case and sign patterns that require semipositivity are characterized.
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We are pleased to dedicate this work to the very fond memory of Miroslav Fiedler, who helped to shape this subject and our views on it
This work supported in part by NSF Grant DMS-0751964.
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Dorsey, J., Gannon, T., Johnson, C.R. et al. New results about semi-positive matrices. Czech Math J 66, 621–632 (2016). https://doi.org/10.1007/s10587-016-0282-x
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DOI: https://doi.org/10.1007/s10587-016-0282-x