Condensed Cramer rule for some restricted quaternion linear equations
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Publication:426308
DOI10.1016/j.amc.2011.08.038zbMath1248.15016OpenAlexW2010665112MaRDI QIDQ426308
Guang-Jing Song, Qing-Wen Wang
Publication date: 11 June 2012
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2011.08.038
Theory of matrix inversion and generalized inverses (15A09) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Linear equations (linear algebraic aspects) (15A06)
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Cites Work
- Cramer rule for the unique solution of restricted matrix equations over the quaternion skew field
- Cramer's rule for some quaternion matrix equations
- The quaternion-based three-dimensional beam theory
- Rank equalities related to the generalized inverses \(A_{T,S}^{(2)}\), \(B_{T_1,S_1}^{(2)}\) of two matrices \(A\) and \(B\)
- On the \((p,q)\) outer generalized inverse in Banach algebra
- A Cramer rule for minimum-norm (T) least-squares (S) solution of inconsistent linear equations
- A Cramer rule for least-norm solutions of consistent linear equations
- A Cramer rule for the least-norm, least-squared-error solution of inconsistent linear equations
- Inverse matrix and properties of double determinant over quaternion field
- Quaternionic determinants
- A characterization and representation of the generalized inverse \(A_{T,S}^{(2)}\) and its applications
- The reverse order law for the generalized inverse \(A^{(2)}_{T,S}\)
- Cramer's rule for quaternionic systems of linear equations
- Determinantal representations of the Moore–Penrose inverse over the quaternion skew field and corresponding Cramer's rules
- Determinantal representation of the generalized inverse\bi A_{T,S}^{(2)}over integral domains and its applications
- On determinantal representation for the generalized inverseA(2)T,S and its applications
- The Generalized Inverse A(2)T, Sof a Matrix Over an Associative Ring
- Analogs of the adjoint matrix for generalized inverses and corresponding Cramer rules
- Definition of determinant and cramer solutions over the quaternion field
- The quaternionic determinant
- Finite algorithms for the (2)-generalized inverse
- A Short Proof of Cramer's Rule
- Outer Generalized Inverses in Rings