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Strong B-T inverse.

Sanzhang Xu1, Yuyue Huang1, Jinyong Wu2

  • 1Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian 223003, China.

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|October 21, 2024
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Summary
This summary is machine-generated.

Researchers introduced a new matrix inverse, the strong B-T inverse, generalizing the B-T inverse using Hartwig-Spindelböck decomposition. Its properties and conditions were explored using column and null spaces.

Keywords:
15A09B-T inverseGeneralized inverseHartwig-Spindelböck decomposition

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Area of Science:

  • Linear Algebra
  • Matrix Theory

Background:

  • The B-T inverse is a significant concept in generalized matrix inverses.
  • Understanding new generalized inverses is crucial for advancing matrix theory.

Purpose of the Study:

  • To introduce and investigate a new type of matrix inverse, the strong B-T inverse.
  • To establish the relationship between the strong B-T inverse and other existing matrix inverses.
  • To derive necessary and sufficient conditions for the strong B-T inverse.

Main Methods:

  • Utilizing the Hartwig-Spindelböck decomposition.
  • Analyzing the properties of the strong B-T inverse.
  • Employing concepts of column spaces and null spaces.

Main Results:

  • The strong B-T inverse was defined as a generalization of the B-T inverse.
  • Relationships between the strong B-T inverse and other matrix inverses were established.
  • Sufficient and necessary conditions for the strong B-T inverse were derived using column and null spaces.

Conclusions:

  • The strong B-T inverse offers a novel extension within the field of generalized matrix inverses.
  • The derived conditions provide a deeper understanding of this new inverse type.
  • This work contributes to the theoretical framework of matrix analysis.