nonsingular－a little sad a little happy a littleyu

Apr 15 Thu 2010 22:25
nonsingular

close

We call a linear transformation T non-singular if Tx=0 implies x=0.

Let T be a linear transformation form V into W.
Then T is non-singular
if and only if
T carries each linearly independent subset of V
onto a linearly independent subset of W.

簡單的小証明
但是卻有一個鬼東西
以前我們都說 nonsingular 就是可逆矩陣
雖然聖經本有稍稍稍稍微提到
但是我們還是習慣了說
就是可逆
不過這邊給出了nonsingular 的定義
不要再認為是可逆矩陣摟!!