Abstract
For any , is called the j-conjugate matrix of A. If , A is called a j-self-conjugate matrix. If , A is called an anti j-self-conjugate matrix. By using the complex representation of quaternion matrices, the Moore–Penrose generalized inverse and the Kronecker product of matrices, we derive the expressions of the least squares solution with the least norm, the least squares j-self-conjugate solution with the least norm, and the least squares anti j-self-conjugate solution with the least norm of the matrix equation over the skew field of quaternions, respectively.
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