推 KAINTS:感謝!! 02/04 08:36
※ 引述《KAINTS (RUKAWA)》之銘言：
: T/F
: 假設A,B兩個矩陣分別是 n*k , k*m,如果A,B皆為行獨立,
: 則AB也為行獨立
Suppose that A, B are n*k, k*m matrices with linearly
independent columns, respectively. Let ABx = 0 for
x in F^m (F, a field). Because of linearly independence
of columns of A, that is, ker(A) = {0},
A(Bx) = 0 implies Bx = 0. Similarly, Bx = 0 implies x = 0
since B has linearly independent columns. By the above,
ABx = 0 implies x = 0, in other words, AB has linearly
independent columns.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 114.37.135.131