[線代] diagonally dominant

看板Math作者handsomepow (handsomepow)時間14年前 (2011/11/24 20:17)推噓2(2推 0噓 9→)

留言11則, 2人參與討論串1/2 (看更多)

Matrix A=[a_ij] 屬於 R^n*n is called strictly column diagonally dominant or diagonally dominant for short, if n |a_ii| > sigma |a_ji|. i=1,j=1 Assume after one step of Gaussian elimination, the matrix A has the following form [a_11 (a_1)^T] [ 0 A_2 ] wwwwwwwwwwwwwwww (這裡(a_1)^T 看不懂是啥東西) (a) Show that A is nonsingular. Hint: Use Gershgorin's theorem. (b) Show that matrix A_2 is still strictly column diagonally dominant, i.e.,Gaussian elimination with partial pivoting does not actually permute any rows. 請求高手教我解這題 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 111.242.6.101

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TWN2

11/25 04:43, , 1^F

11/25 04:43, 1^F

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TWN2

11/25 04:45, , 2^F

11/25 04:45, 2^F

不太懂怎使用定理跟定義可以請T大講解嗎謝謝 ※ 編輯: handsomepow 來自: 111.242.6.101 (11/25 08:02)

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TWN2

11/25 08:36, , 3^F