[微方] 證明題
Ax=b when det A=0
(a)Suppose that A is a real-valued n*n matrix.Show that (Ax,y)=(x,A的轉置y)for
any vectors x and y.
(b)If A is not necessary real, show that (Ax,y)=(x,A*y)for any vectors x and y.
(*不是乘,是A*乘y)
(c)If A is Hermitian, show that (Ax,y)=(x,Ay)for any vectors x and y.
順便借問一題線代
┌-1 4 2 ┐ ┌ 1-2-1 ┐
A=│-1 3 1 │ eigenvalue=1→ A-I=│ 0 0 0 │
└-1 2 2 ┘ └ 0 0 0 ┘
┌ 0 3 1 ┐ ┌ 1 0 0 ┐
B=│-1 3 1 │ eigenvalue=1→ B-I=│ 0 1 0 │
└ 0 1 1 ┘ └ 0 0 0 ┘
A的rank=1 dim EA(1)=2
B的rank=2 dim EB(1)=1
請問dim要怎麼看??
謝謝
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