The pseudoinverse of an $r$-circulant matrix
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- by W. T. Stallings and T. L. Boullion PDF
- Proc. Amer. Math. Soc. 34 (1972), 385-388 Request permission
Abstract:
It is shown that the Moore-Penrose pseudoinverse ${C^ + }$ of an r-circulant matrix C is always the conjugate transpose of an r-circulant matrix. In addition, necessary and sufficient conditions are given for ${C^ + }$ to be an s-circulant matrix. Finally, a method for calculating ${C^ + }$ is given.References
- C. M. Ablow and J. L. Brenner, Roots and canonical forms for circulant matrices, Trans. Amer. Math. Soc. 107 (1963), 360–376. MR 155841, DOI 10.1090/S0002-9947-1963-0155841-7
- S. Charmonman and R. S. Julius, Explicit inverses and condition numbers of certain circulants, Math. Comp. 22 (1968), 428–430. MR 226831, DOI 10.1090/S0025-5718-1968-0226831-9 G. H. Worm, Explicit solutions for quadratic minimization problems, Doctoral Dissertation, University of Tennessee, Knoxville, Tennessee, 1971.
- Ivan Niven and Herbert S. Zuckerman, An introduction to the theory of numbers, John Wiley & Sons, Inc., New York-London, 1960. MR 0114786
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 34 (1972), 385-388
- MSC: Primary 15A09
- DOI: https://doi.org/10.1090/S0002-9939-1972-0296082-3
- MathSciNet review: 0296082