Conjugate Gradient Algorithm for the Symmetric Arrowhead Solution of Matrix Equation AXB=C
نویسندگان
چکیده
2 A denote the transpose, Moore-Penrose generalized inverse, Frobenius norm and Euclid norm, respectively. For any , m n A B R , , 0 T A B trace B A denotes the inner product of A and B . Therefore, m n R is a complete inner product space endowed with 2 , A A A . For any non-zero matrices 1 2 , , , m n k A A A R , if , T j i i A A trace A 0 j A i j , then it is easy to verify that 1 2 , , , k A A A are linearly independent and orthogonal. Proposition 1. Let , n n A B R , then ( ) ( ); T trace A trace A ( ) ( ) trace AB trace BA ( ) ( ) ( ) trace A B trace A trace B
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