Inversion of isoclinal matrices
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- by Leroy J. Derr PDF
- Math. Comp. 26 (1972), 719-721 Request permission
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
- T. S. Chow, A class of Hessenberg matrices with known eigenvalues and inverses, SIAM Rev. 11 (1969), 391–395. MR 252407, DOI 10.1137/1011065
- Leroy J. Derr, Triangular matrices with the isoclinal property, Pacific J. Math. 37 (1971), 41–43. MR 320031
- D. K. Faddeev and V. N. Faddeeva, Computational methods of linear algebra, W. H. Freeman and Co., San Francisco-London, 1963. Translated by Robert C. Williams. MR 0158519
- Alston S. Householder, The theory of matrices in numerical analysis, Blaisdell Publishing Co. [Ginn and Co.], New York-Toronto-London, 1964. MR 0175290
- Studies in real and complex analysis, Studies in Mathematics, Vol. 3, Mathematical Association of America, Buffalo, N.Y.; Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. I. I. Hirschman, Jr., editor. MR 0183600
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Math. Comp. 26 (1972), 719-721
- MSC: Primary 65F30
- DOI: https://doi.org/10.1090/S0025-5718-1972-0327016-9
- MathSciNet review: 0327016