Inversion of isoclinal matrices

Author:
Leroy J. Derr

Journal:
Math. Comp. **26** (1972), 719-721

MSC:
Primary 65F30

DOI:
https://doi.org/10.1090/S0025-5718-1972-0327016-9

MathSciNet review:
0327016

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Abstract: Triangular matrices (over the reals), whose elements satisfy , 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.

**[1]**T. S. Chow, ``A class of Hessenberg matrices with known eigenvalues and inverses,''*SIAM Rev.*, v. 11, 1969, pp. 391-395. MR**40**#5627. MR**0252407 (40:5627)****[2]**L. J. Derr, ``Triangular matrices with the isoclinal property,''*Pacific J. Math.*, v. 37, 1971, pp. 41-14. MR**0320031 (47:8572)****[3]**D. K. Faddeev & V. N. Faddeeva,*Computational Methods of Linear Algebra*, Fizmatgiz, Moscow, 1960; English transl., Freeman, San Francisco, Calif., 1963, pp. 161-163. MR**28**#1742; #4659. MR**0158519 (28:1742)****[4]**A. S. Householder,*The Theory of Matrices in Numerical Analysis*, Blaisdell, Waltham, Mass., 1964. MR**30**#5475. MR**0175290 (30:5475)****[5]**I. I. Hirschman, JR. (Editor),*Toeplitz Matrices, Studies in Real and Complex Analysis*, Math. Assoc. Amer.; Prentice-Hall, Englewood Cliffs, N. J., 1965, pp. 179-209. MR**32**#1080. MR**0183600 (32:1080)**

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DOI:
https://doi.org/10.1090/S0025-5718-1972-0327016-9

Article copyright:
© Copyright 1972
American Mathematical Society