這是可逆矩陣嗎?

給定

A=\begin{bmatrix}  4563&2138&8978&1026\\  7890&1237&8662&2048\\  1140&3450&9975&7824\\  2884&6782&3686&4589  \end{bmatrix}

如果不實際算出矩陣秩或行列式,我們可以從矩陣型態判定 A 是可逆矩陣嗎?

In problem solving, as in street fighting, rules are for fools: do whatever works–don’t just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions.

─Sanjoy Mahajan, Street-Fighting Mathematics

歡迎讀者朋友提供快打旋風 (street fighter) 的作法。

This entry was posted in 隨筆雜談 and tagged . Bookmark the permalink.

1 Response to 這是可逆矩陣嗎?

  1. ccjou says:

    此例 A 確實可逆,問題是如何證明 \det A\neq 0

    利用奇偶性可判定 \det A\neq 0,詳細請見“利用模算術判定可逆矩陣”:
    https://ccjou.wordpress.com/2012/10/31/%E5%88%A9%E7%94%A8%E6%A8%A1%E7%AE%97%E8%A1%93%E5%88%A4%E5%AE%9A%E5%8F%AF%E9%80%86%E7%9F%A9%E9%99%A3/

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