Efficient characterization for I{2} and M{2}

ZHENG Dao-Sheng

doi:10.3969/j.issn.1000-5641.2015.01.005

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Mar. 2015

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ZHENG Dao-Sheng. Efficient characterization for I{2} and M{2}[J]. Journal of East China Normal University (Natural Sciences), 2015, (1): 42-50. doi: 10.3969/j.issn.1000-5641.2015.01.005

Citation:

ZHENG Dao-Sheng. Efficient characterization for I{2} and M{2}[J]. Journal of East China Normal University (Natural Sciences), 2015, (1): 42-50. doi: 10.3969/j.issn.1000-5641.2015.01.005

ZHENG Dao-Sheng. Efficient characterization for I{2} and M{2}[J]. Journal of East China Normal University (Natural Sciences), 2015, (1): 42-50. doi: 10.3969/j.issn.1000-5641.2015.01.005

Citation:

ZHENG Dao-Sheng. Efficient characterization for I{2} and M{2}[J]. Journal of East China Normal University (Natural Sciences), 2015, (1): 42-50. doi: 10.3969/j.issn.1000-5641.2015.01.005

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Efficient characterization for I{2} and M{2}

doi: 10.3969/j.issn.1000-5641.2015.01.005

ZHENG Dao-Sheng^,

Received Date: 2013-10-01
Publish Date: 2015-01-25

Abstract

Abstract

An important characterization formula for M{2} was given by Stewart where M 2 Cmn. But this formula contains redundant arbitrary parameters, and therefore is nonefficient. This paper, by using the matrix full rank decomposition, showed that for a proper subset of I{2}s, which is denoted as B1, the redundant arbitrary parameters in Stewarts formula can be eliminated, and I{2}s is a union set of its certain subsets, and each of the subsets is 2-norm isometry with B1. Finally, the efficient characterization fonmulas for I{2}s, I{2} and M{2} are obtained respectively. An algorithm was provided that can be used to compute any element of I{2}s, and avoid the repeat computation work for each element of I{2}s.

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References(1)

References

[1]

BEN-ISRAEl A, GREVIllE T N E. Generalized Inverse: Theory and Applications [M]. 2nd ed., New York: Spring Verlag, 2003.
DONG Z Q, YANG H. Characteristics of {2}-generalized inverses and some problems on partitioned matrices [J]. Pure Appl Math (Chinese), 1998, 14: 87-92.
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SEWART G W. Projectors and generalized inverses [R]. Technical Report, TNN-97. [s.l.]: University of Texas at Austin Computation Center, 1969.

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