標題:
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Linear Algebra
發問:
Let A be an m X n matrix, B be an n X m matrix. If n
最佳解答:
Thm: A matrix M is invertible Null of M = 0 (trivial vector sapce) So, if we can find a nonzero vector x, Mx=0, then M is not invertible. Now, B is nxm (m>n), consider the system of linear eq. Bx=0, where x in R^m. The linear system Bx=0 has n equations with m variables, then the dim. of {x | Bx=0} >= m-n >0. Thus, we can find a nonzero vector x such that Bx=0, and then ABx=0. i.e. there exists a nonzero vector x, (AB)x=0, so, AB is not invertible. 2009-09-17 00:19:01 補充： 基本原理: Linear mapping 不可能將空間變大(增加dim.) 本題 B: R^m -> R^n 已經將空間 R^m變小了 再來A: R^n -> R^m 不可能 1對1. OK!? 2009-09-17 00:53:12 補充： 物理系有這玩意兒嗎?
其他解答:
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