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Mathematics of Computation

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Inversion of isoclinal matrices


Author: Leroy J. Derr
Journal: Math. Comp. 26 (1972), 719-721
MSC: Primary 65F30
MathSciNet review: 0327016
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Abstract: Triangular matrices (over the reals), whose elements satisfy $ {a_{i,j}} = {a_{i + 1,j + 1}}$, can be mapped algebraically into the rational functions to facilitate determination of inverses and factors of the matrices. It is further shown in this note that these methods can be extended to the nontriangular forms to obtain inverses or demonstrate singular cases. Applications are made to certain matrices of Hessenberg type.


References [Enhancements On Off] (What's this?)

  • [1] T. S. Chow, A class of Hessenberg matrices with known eigenvalues and inverses., SIAM Rev. 11 (1969), 391–395. MR 0252407
  • [2] Leroy J. Derr, Triangular matrices with the isoclinal property, Pacific J. Math. 37 (1971), 41–43. MR 0320031
  • [3] D. K. Faddeev and V. N. Faddeeva, Computational methods of linear algebra, Translated by Robert C. Williams, W. H. Freeman and Co., San Francisco-London, 1963. MR 0158519
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DOI: https://doi.org/10.1090/S0025-5718-1972-0327016-9
Article copyright: © Copyright 1972 American Mathematical Society