[理工] [工數] [矩陣] 正交
Is the following matrix orthogonal? Why? (10%)
[ 1 ]
[ --- - √2/3 0 ]
[ √3 ↓ ]
[ (-√2/√3) ]
[ ]
[ 1 1 -1 ]
[ --- --- --- ]
[ √3 √6 √2 ]
[ ]
[ ]
[ 1 1 1 ]
[ --- --- --- ]
[ √3 √6 √2 ]
----------------------------------------------
我計算過程
[ 2 -√2 √2 ]
[ ---- ----- ---- ]
[ √12 √6 √6 ]
[ ]
[ ]
[ -2 1 -2 ]
[ --- ---- ---- ]
[ √6 √6 √6 ]
[ ]
[ -2 2 ]
[ 0 --- ---- ]
[ √18 √18 ]
A^-1 = ------------------------------- <===(計算冗長,算到有點恍神
|A| = 1
根據正交定義A^T = A^-1
故
(1)此矩陣不為正交
(2)因為A^T≠A^-1
請問有其他方法算這題的反矩陣嗎?
還有我的答案(1)(2)的觀念是對的嗎??
麻煩各位幫忙了謝謝
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