Explicit representation formulas for the minimum norm least squares solutions of some quaternion matrix equations

Abstract

Within the framework of the theory of the column and row determinants, we obtain explicit representation formulas (analogs of Cramer's rule) for the minimum norm least squares solutions of quaternion matrix equations AX = B, XA = B and AXB = D.

High-Order Iterative Methods for the DMP Inverse

“…For a nonnegative integer , if rank( 푙+1 ) = rank( 푙 ), then is called the index of and ind( ) = . In recent years, the generalized inverse has been applied in many fields of engineering and technology, such as control [1], the least squares problem [2,3], matrix decomposition [4], image restoration, statistics (see [5]), and preconditioning [6][7][8]. In particular, {2}-inverse plays an important role in stable approximations of ill-posed problems (see [1,9]) and in linear and nonlinear problems [6,10].…”

Cramer’s Rules for the System of Two-Sided Matrix Equations and of Its Special Cases

“…Within the framework of columnrow determinants, determinantal representations of various kind of generalized inverses, (generalized inverses) solutions of quaternion matrix equations recently have been derived as by the author (see, e.g. [18][19][20][21][22]) so by other researchers (see, e.g. [23][24][25][26]).…”

The Column and Row Immanants Over A Split Quaternion Algebra

“…The theory of the row and column determinants was introduced in [2,3] for matrices over the quaternion non-split algebra. This theory over the quaternion skew field is being actively developed as by the author [4]- [6], and others (see, for ex. [7]- [9]).…”