Least-norm and Extremal Ranks of the Least Square Solution to the Quaternion Matrix Equation AXB=C Subject to Two Equations (Q3191849)

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English	Least-norm and Extremal Ranks of the Least Square Solution to the Quaternion Matrix Equation AXB=C Subject to Two Equations	scientific article

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title

Least-norm and Extremal Ranks of the Least Square Solution to the Quaternion Matrix Equation AXB=C Subject to Two Equations (English)

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25 September 2014

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zbMATH Keywords

matrix equations

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quaternion matrices

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least squares

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maximal rank

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minimal rank

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consistency

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MaRDI profile type

MaRDI publication profile

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cites work

Nonnegative definite and positive definite solutions to the matrix equationAXA*=B

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Regularization of Singular Systems by Derivative and Proportional Output Feedback

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Inertia and Rank Characterizations of Some Matrix Expressions

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Minimum norm regularization of descriptor systems by mixed output feedback

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On the symmetric solutions of linear matrix equations

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The spectral theorem in quaternions

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The expansion problem of anti-symmetric matrix under a linear constraint and the optimal approximation

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On the symmetric solutions of a linear matrix equation

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Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations

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Least-squares solution with the minimum-norm for the matrix equation \((A\times B,G\times H) = (C,D)\)

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Ranks of least squares solutions of the matrix equation \(AXB=C\)

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The matrix equations \(AX=C\), \(XB=D\)

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A pair of simultaneous linear matrix equations \(A_ 1XB_ 1=C_ 1,A_ 2XB_ 2=C_ 2\) and a matrix programming problem

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Two matrix-based proofs that the linear estimator \(G y\) is the best linear unbiased estimator

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PARTIALLY SUPERFLUOUS OBSERVATIONS

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Upper and lower bounds for ranks of matrix expressions using generalized inverses

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Ranks of Solutions of the Matrix Equation AXB = C

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On equality and proportionality of ordinary least squares, weighted least squares and best linear unbiased estimators in the general linear model

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On the matrix equation \(AX=B\) with applications to the generators of a controllability matrix

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\(P\)-(skew)symmetric common solutions to a pair of quaternion matrix equations

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Ranks and the least-norm of the general solution to a system of quaternion matrix equations

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Extreme ranks of the solution to a consistent system of linear quaternion matrix equations with an application

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Extremal ranks of a quaternion matrix expression subject to consistent systems of quaternion matrix equations with applications

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Extreme ranks of a linear quaternion matrix expression subject to triple quaternion matrix equations with applications

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Least squares Hermitian solution of the matrix equation \((AXB,CXD)=(E,F)\) with the least norm over the skew field of quaternions

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full work available at URL

https://doi.org/10.1142/s100538671400039x

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Identifiers

zbMATH Open document ID

1303.15018

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DOI

10.1142/S100538671400039X

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:3191849