Czechoslovak Mathematical Journal

, Volume 65, Issue 2, pp 537–544 | Cite as

Nested matrices and inverse M-matrices



Given a sequence of real or complex numbers, we construct a sequence of nested, symmetric matrices. We determine the LU- and QR-factorizations, the determinant and the principal minors for such a matrix. When the sequence is real, positive and strictly increasing, the matrices are strictly positive, inverse M-matrices with symmetric, irreducible, tridiagonal inverses.


nested matrix tridiagonal matrix inverse M-matrix principal minor determinant QR-factorization 

MSC 2010

15A15 15A09 15B0 


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    A. Berman, R. J. Plemmons: Nonnegative Matrices in the Mathematical Sciences. Classics in Applied Mathematics 9, SIAM, Philadelphia, 1994.Google Scholar
  2. [2]
    The On-Line Encyclopedia of Integer Sequences., 2010.
  3. [3]
    E. W. Weisstein: Fibonorial. From MathWorld—A Wolfram Web Resource,

Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2015

Authors and Affiliations

  1. 1.Mathematics DepartmentPacific Lutheran UniversityTacomaUSA

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