Re: [線代] 方陣 反矩陣
※ 引述《otomoyox (想)》之銘言：
: 請問該如何證明方陣只要具左反矩陣或是右反矩陣就是inbertible呢?
: 知道這是對的，但卻想不出具體的證明
: 煩請各位大大幫忙解惑
: 感謝<(＿ ＿)>
Let A be an n*n matrix with a left inverse, say B.
Then AX = 0 => X = 0, since X = IX = (BA)X = B(AX).
Hence, A is invertible.
On the other hand, let A be an n*n matrix with right inverse, say C.
Then C has a left inverse => C is invertible. (by the above proof)
Hence, C^(-1) = A
=> A is invertible with inverse C.
Q.E.D.
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※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 1.34.27.65
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09/23 13:57, , 1F
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利用定理: A is invertible if and only if AX = 0 has only trivial solution.
所以AX = 0 是我們的假設.
※ 編輯: CFE220 來自: 1.34.27.65 (09/23 14:02)
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討論串 (同標題文章)