IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-981-15-2059-4_5.html

Plane Stochastic Tensors

In: Theory and Computation of Complex Tensors and its Applications

Author

Listed:
  • Maolin Che

    (Southwestern University of Finance and Economics, School of Economics Mathematics)

  • Yimin Wei

    (Fudan University, School of Mathematical Sciences)

Abstract

We study combinatorial properties of nonnegative tensors. We make the following contributions: (1) we obtain equivalent conditions for sign nonsingular tensors and relationships between the combinatorial determinant and the permanent of nonnegative tensors, in Theorems 5.2.1 and 5.2.2; (2) the sets of plane stochastic tensors and totally plane stochastic tensors are closed, bounded and convex sets, and an nonnegative tensor has a plane stochastic pattern if and only if its positive entries are contained in a positive diagonal, in Lemma 5.3.1 and Theorem 5.3.2; (3) from a nonnegative tensor, we propose a normalization algorithm which converges to a plane stochastic tensor, in Theorem 5.3.8; (4) we discuss the boundlessness of the diagonal products of any nonnegative tensor and obtain a probabilistic algorithm after Theorem 5.4.4 for locating a positive diagonal in a (0, 1)-tensor; (5) we explore the axial N-index assignment problem via the set of plane stochastic tensors in Sect. 5.5.

Suggested Citation

  • Maolin Che & Yimin Wei, 2020. "Plane Stochastic Tensors," Springer Books, in: Theory and Computation of Complex Tensors and its Applications, chapter 0, pages 117-146, Springer.
    • Handle: RePEc:spr:sprchp:978-981-15-2059-4_5
    DOI: 10.1007/978-981-15-2059-4_5
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-981-15-2059-4_5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.