Multiple LU factorizations of a singular matrix |
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Authors: | Froilán M Dopico |
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Institution: | a Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain b Department of Mathematics, The College of William and Mary, Williamsburg, VA 23187-8795, USA |
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Abstract: | A singular matrix A may have more than one LU factorizations. In this work the set of all LU factorizations of A is explicitly described when the lower triangular matrix L is nonsingular. To this purpose, a canonical form of A under left multiplication by unit lower triangular matrices is introduced. This canonical form allows us to characterize the matrices that have an LU factorization and to parametrize all possible LU factorizations. Formulae in terms of quotient of minors of A are presented for the entries of this canonical form. |
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Keywords: | 15A23 15A21 65F30 |
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