problem about matrices

👨🏻‍🏫 學術台數學

doraemonpaul

2007-04-09 10:07 pm

If Aⁿ = B , where A and B are matrices. Can I write as A = ⁿ√B or A = B^(1/n) ? Why?

回答 (4)

阿一

2007-04-13 4:18 pm

✔ 最佳答案

可以, 你take log都仲得
不過, 所有o野都要用matrix o既做法, 當有o的property係會同integer arithmetic類似

take p-th root唔係咁簡單
http://www.springerlink.com/content/jq62520252q3978u

http://en.wikipedia.org/wiki/Square_root_of_a_matrix
http://en.wikipedia.org/wiki/Logarithm_of_a_matrix

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Andrew

2007-05-17 5:05 pm

如果寫一寫Cholesky Decomposition 和只限Positive Definite會更好。

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volga

2007-04-09 11:39 pm

唔可以

因為matrix的次方不是單純的乘法，matrix的乘法與一般的乘法唔同

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Thomas

2007-04-09 11:39 pm

if Aⁿ = B
you can only write AAA...A = B (n terms of A)

by defination, Matrix have not fractional index.

參考: me

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