半正定自共轭四元数矩阵广义逆的.pdfVIP

392 Vol.39, No. 2 19963 ACTA MATHEMATICA SINICA Mar., 1996 d
epzoi gxnabvtq  (PKLP 363000) w:   L¨owner  0 ≤ B ≤ A.  H(n, ≥)    B{1; ≥; s; ≥ A(1)}  !#$%()* +,-. i) ∀B (1) ∈ B{1; ∗}, A{1; ∗; ≤ B (1)} = ∅; ii) 0 ≤ B (1,2) ≤ A(1,2) ; iii) ∀A(1,2) ∈ A{1, 2; ≥}, B{1, 2; ≥; ≤ A(1,2) } /01% 2 fh345678  L¨owner 9:; RQ L¨owner pNRBa [1−8] , z [9, 10] l EBBVZnLgnjFJSxmBBVZ ahX B{1; ≥; s; ≥ A(1)} QpaDV gAh z [10, 11] vfB H(n, ∗, r) = {X ∈ H (n, ∗) | rank X = r}, H(n, ≥ , r) = {X ∈ H (n, ≥) | rank X = r}; I A ∈ H (n, ≥), v A{i, · · · , j; ∗} = {X ∈ A{i, · · · , j} | X ∗ = X }, A{i, · · · , j; ∗; r} = {X ∈ A{i, · · · , j; ∗} | rank X = r}, A{i, · · · , j; ∗; r; ≤ C } = {X ∈ A{i, · · · , j; ∗; r | C − X ∈ H(n, ≥)}, C ∈ H(n, ∗). tv Rr (A) = {AX | X ∈ Hn ×1}, L A ∈ Hm ×n ; “rs” SKL [12]. ≤ xMzLBEZDV [11] B 1 p 1 pE yk 1 I A = P ∗−1 D 0 P −1, P ∈ GL (H), D = diag (λ , · · · , λ ) 0, n 1 r 0 0 −1 D X ∗ r ×(n−r) A{1; ∗; t} = P ∗ ∗ P X ∈ H , Y ∈ H(n − r, ∗, t − r) , X X DX + Y t = r, r + 1, · · · , n; (1) −1 D X ∗ r ×(n−r)