[理工] 線代 找nullity

看板Grad-ProbAsk作者時間15年前 (2010/12/16 22:26), 編輯推噓3(306)
留言9則, 3人參與, 最新討論串1/1
An n*n tridiagonal matrix. Let V be the vector space of all n*n real tridiagonal matrices under the operations of matrix addition and multiplication of a matrix by a real number, and T:V -> V be the linear operator defined by T(A)=(A+A^T)/2 for all A in V. Find the nullity. ------------------------------------------ 我覺得是n-2 但是周易的解答寫n-1 麻煩大家為我解惑 謝謝 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 114.42.169.46

12/16 23:17, , 1F
應該是N*(N-1)/2吧
12/16 23:17, 1F

12/16 23:18, , 2F
T(A)=(A+A^T)/2=O => A^T= -A 主對角線是0
12/16 23:18, 2F

12/16 23:19, , 3F
對角線之外對偁差個負號 所以只算對角線上方的
12/16 23:19, 3F

12/16 23:22, , 4F
A為tridiagonal且A=-A^T
12/16 23:22, 4F

12/16 23:24, , 5F
因為上下成負一倍 只算主對角線上面那條 數目是n-1個
12/16 23:24, 5F

12/16 23:25, , 6F
可能你想成那條有n-2個了你從最右上角開始想1,2...n-1,n
12/16 23:25, 6F

12/16 23:25, , 7F
我沒看到tridiagonal 樓上正確
12/16 23:25, 7F

12/17 20:24, , 8F
不好意思 我還是不懂 嘗試了3階算 但我算出的nullity=1
12/17 20:24, 8F

12/17 20:26, , 9F
我看到GamesWang的回信了 謝謝 我了解了
12/17 20:26, 9F
文章代碼(AID): #1D2Y6DDa (Grad-ProbAsk)