(d) Show that if L E Mn is upper triangular, th LL, and argue that IAgIP-lAollF, where IIA]IF、/tr(ATA) represents...
(d) Show that if L E Mn is upper triangular, th LL, and argue that IAgIP-lAollF, where IIA]IF、/tr(ATA) represents the Frobenius norm of A, and tr(A)-Σ.1 A" is the trace of A. (e) Assu me that an upper triangular matrix L has the block structure し11 し12 0 In with the size of the Ln blook being m × m. Let A-LTL, and λ = LLT. Show that tr(A (1 : m, 1 : m))-tr(A(1 : m, 1 : m)) + (f) Use (d) and (e) to show that for every fixed m-1,2,. . , n, the sequence tr(A&(1 : m,1: m)) is increasing and bounded with respecet to k. (8) Show that the diagonal entries of Ak converge as k-oo, and use (2) t off-diagonal entries of Ak converge to 0 as k → oo. o show that the l
(d) Show that if L E Mn is upper triangular, th LL, and argue that IAgIP-lAollF, where IIA]IF、/tr(ATA) represents the Frobenius norm of A, and tr(A)-Σ.1 A" is the trace of A. (e) Assu me that an upper triangular matrix L has the block structure し11 し12 0 In with the size of the Ln blook being m × m. Let A-LTL, and λ = LLT. Show that tr(A (1 : m, 1 : m))-tr(A(1 : m, 1 : m)) + (f) Use (d) and (e) to show that for every fixed m-1,2,. . , n, the sequence tr(A&(1 : m,1: m)) is increasing and bounded with respecet to k. (8) Show that the diagonal entries of Ak converge as k-oo, and use (2) t off-diagonal entries of Ak converge to 0 as k → oo. o show that the l