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The Pseudoinverse of an $r$-Circulant Matrix

W. T. Stallings and T. L. Boullion
Proceedings of the American Mathematical Society
Vol. 34, No. 2 (Aug., 1972), pp. 385-388
DOI: 10.2307/2038377
Stable URL: http://www.jstor.org/stable/2038377
Page Count: 4
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Pseudoinverse of an $r$-Circulant Matrix
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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.

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