※ 引述《thank1984 (thankakimo)》之銘言：
: 是非題:
: a) Every vector space that is spanned by a finite set has a basis
: True
: b) Every subspace of a finite-dimensional space is finite-dimensional
: False
設V為finite-dimensional space S為其subspace
=> S包含於V => 0≦dim(S)≦dim(V)
=> S is finite-dimensional
所以本題為true
: c) The only entries of an elementary matrix are zeros and ones
: True
(3)
R 為elementary matrix，但其元素不全為0或1
12
補充：an elementary matrix有3種
(k) (k)
(1)R (2)R (3)R 其中k€F
ij i ij
本題為False
: d) The sum of two n*n elementary matrices is an elementray matrix.
: False
: e) Every finite-dimensional inner product space posseses an
: orthornormal basis.
: False
Every finite-dimensional inner product space的basis
皆可利用Gram-Schmidt orthogonal process得到一組orthornormal basis
本題為true
: 以上是非題答案小弟都不太確定 所以請大大們幫小弟檢查一下是否有寫錯
: 麻煩各位大大了 感謝
有錯麻煩各位幫忙訂正
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 125.233.23.162