@article{(Open Science Index):https://publications.waset.org/pdf/17082,
	  title     = {Minimization Problems for Generalized Reflexive and Generalized Anti-Reflexive Matrices},
	  author    = {Yongxin Yuan},
	  country	= {},
	  institution	= {},
	  abstract     = {Let R ∈ Cm×m and S ∈ Cn×n be nontrivial unitary involutions, i.e., RH = R = R−1 = ±Im and SH = S = S−1 = ±In. A ∈ Cm×n is said to be a generalized reflexive (anti-reflexive) matrix if RAS = A (RAS = −A). Let ρ be the set of m × n generalized reflexive (anti-reflexive) matrices. Given X ∈ Cn×p, Z ∈ Cm×p, Y ∈ Cm×q and W ∈ Cn×q, we characterize the matrices A in ρ that minimize AX−Z2+Y HA−WH2, and, given an arbitrary A˜ ∈ Cm×n, we find a unique matrix among the minimizers of AX − Z2 + Y HA − WH2 in ρ that minimizes A − A˜. We also obtain sufficient and necessary conditions for existence of A ∈ ρ such that AX = Z, Y HA = WH, and characterize the set of all such matrices A if the conditions are satisfied. These results are applied to solve a class of left and right inverse eigenproblems for generalized reflexive (anti-reflexive) matrices.
},
	    journal   = {International Journal of Mathematical and Computational Sciences},
	  volume    = {7},
	  number    = {5},
	  year      = {2013},
	  pages     = {890 - 896},
	  ee        = {https://publications.waset.org/pdf/17082},
	  url   	= {https://publications.waset.org/vol/77},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 77, 2013},
	}