A Drazin inverse for rectangular matrices |
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| Authors: | Randall E Cline TNE Greville |
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| Institution: | Mathematics Department and the Computing Center University of Tennessee Knoxville, Tennessee 37916 USA;Mathematics Research Center University of Wisconsin-Madison Madison, Wisconsin 53706 USA |
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| Abstract: | The definition of the Drazin inverse of a square matrix with complex elements is extended to rectangular matrices by showing that for any B and W,m by n and n by m, respectively, there exists a unique matrix, X, such that (BW)k=(BW)k+1XW for some positive integer k, XWBWX = X, and BWX = XWB. Various expressions satisfied by B, W,X and related matrices are developed. |
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