Introducing the class of semidoubly stochastic matrices : a novel scaling approach for rectangular matrices

Knight, Philip A. and le Gorrec, Luce and Mouysset, Sandrine and Ruiz, Daniel (2023) Introducing the class of semidoubly stochastic matrices : a novel scaling approach for rectangular matrices. SIAM Journal on Matrix Analysis and Applications, 44 (4). pp. 1731-1748. ISSN 0895-4798 (https://doi.org/10.1137/22M1519791)

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Abstract

It is easy to verify that if A is a doubly stochastic matrix, then both its normal equations AAT and ATA are also doubly stochastic, but the reciprocal is not true. In this paper, we introduce and analyze the complete class of nonnegative matrices whose normal equations are doubly stochastic. This class contains and extends the class of doubly stochastic matrices to the rectangular case. In particular, we characterize these matrices in terms of their row and column sums and provide results regarding their nonzero structure. We then consider the diagonal equivalence of any rectangular nonnegative matrix to a matrix of this new class, and we identify the properties for such a diagonal equivalence to exist. To this end, we present a scaling algorithm and establish the conditions for its convergence. We also provide numerical experiments to highlight the behavior of the algorithm in the general case.

  • Item type:Article
    ID code:87510
    Dates:
    Date
    Event
    31 December 2023
    Published
    10 November 2023
    Published Online
    27 June 2023
    Accepted
    9 September 2022
    Submitted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:05 Dec 2023 10:34
    Last modified:20 Apr 2024 00:56
    URI:https://strathprints.strath.ac.uk/id/eprint/87510
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