[理工] [線代]-線性映射
1.let T be a linear operator space V of dinension 3 ,and let x be a vector
in V . If p denotes the smallest positive integer such that
3 2
(T-2I) (x)=0 and (T-2I) (x) (T-2I)(x) ,x ar independent vectors,then
What is the matrix presentation of T by the ordered set
2
{(T-2I) (x), (T-2I)(x), x}?
ans: 2 1 0
Ta=[0 2 1 ]
0 0 2
這題我連題目再說什麼都不懂= = 拜託解釋的詳細點 那個p 到底代表什麼?
2.Let A be a real symmetric positive definite n*n matrix
prove that the leading principle submatrices A1 A2.....An of A are all
positive definite(A leading principle submatrix Ar is formed by deleting
the last n-r rows and columns of A)
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