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Matrix Partial Orders Associated with Space Preorder

In: Combinatorial Matrix Theory and Generalized Inverses of Matrices

Author

Listed:
  • K. Manjunatha Prasad

    (Manipal University, Department of Statistics)

  • K. S. Mohana

    (Manipal University, Department of Statistics
    Manipal Institute of Technology, Department of Mathematics)

  • Y. Santhi Sheela

    (Manipal University, Department of Statistics)

Abstract

In this expository article, we discuss some fundamentals of well-known matrix partial orders that are closely associated with space preorder on rectangular matrices. Particularly, we consider partial order defined by space decomposition, star ordering, and minus partial order for our discussion. These relations are closely associated with comparison of column spaces and row spaces of matrices. Results associated with selected matrix relation that are known in the literature along with some interesting observations are put together. At many places, though the proofs of several results are known in the past literature, by part or completely, for better reading purpose, independent proofs are provided.

Suggested Citation

  • K. Manjunatha Prasad & K. S. Mohana & Y. Santhi Sheela, 2013. "Matrix Partial Orders Associated with Space Preorder," Springer Books, in: Ravindra B. Bapat & Steve J. Kirkland & K. Manjunatha Prasad & Simo Puntanen (ed.), Combinatorial Matrix Theory and Generalized Inverses of Matrices, edition 127, pages 195-226, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-1053-5_17
    DOI: 10.1007/978-81-322-1053-5_17
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