Spain, P. G. (1978) Solving an operator equation by iteration. Linear Algebra and its Applications, 20(1), pp. 69-70. (doi: 10.1016/0024-3795(78)90030-7)
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Abstract
It was shown by Bushell [1] that the equation t′xt = x2 has a unique positive-definite solution when t is a real invertible matrix; the proof utilizes the Hilbert projective metric and the Banach fixed-point theorem. I present a simpler proof of a more general result.
| Item Type: | Articles |
|---|---|
| Glasgow Author(s) Enlighten ID: | Spain, Dr Philip |
| Authors: | Spain, P. G. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Linear Algebra and its Applications |
| Publisher: | Elsevier B.V. |
| ISSN: | 0024-3795 |
| ISSN (Online): | 1873-1856 |
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