A*******s 发帖数: 3942 | 1 Wondering if there is any easy-to-implemented algorithm to get the i-th
stochastic root of a transition matrix. Any reference? |
d********t 发帖数: 9628 | 2 啥叫stochastic root?
【在 A*******s 的大作中提到】![](/moin_static193/solenoid/img/up.png) : Wondering if there is any easy-to-implemented algorithm to get the i-th : stochastic root of a transition matrix. Any reference?
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L*******t 发帖数: 2385 | 3 同问,在搞markov Chains?
【在 d********t 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 啥叫stochastic root?
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L*******t 发帖数: 2385 | 4 是eigen value?特征值?
【在 A*******s 的大作中提到】![](/moin_static193/solenoid/img/up.png) : Wondering if there is any easy-to-implemented algorithm to get the i-th : stochastic root of a transition matrix. Any reference?
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L*******t 发帖数: 2385 | 5 http://www.maths.manchester.ac.uk/~lijing/talks/MRSC09.pdf
【在 A*******s 的大作中提到】![](/moin_static193/solenoid/img/up.png) : Wondering if there is any easy-to-implemented algorithm to get the i-th : stochastic root of a transition matrix. Any reference?
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L*******t 发帖数: 2385 | 6 看上个帖子的方法,是先做Jordan分解,然后求Jordan标准型的Root?
【在 A*******s 的大作中提到】![](/moin_static193/solenoid/img/up.png) : Wondering if there is any easy-to-implemented algorithm to get the i-th : stochastic root of a transition matrix. Any reference?
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L*******t 发帖数: 2385 | 7 补充一下,如果你的i是偶数,可以用sqrtm函数get the root in a recursive way.
sqrtm是MATLAB函数
【在 L*******t 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 看上个帖子的方法,是先做Jordan分解,然后求Jordan标准型的Root?
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A*******s 发帖数: 3942 | 8 root matrix that has the stochastic (transition) matrix property (row sum=1
and non negative real elements)
【在 d********t 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 啥叫stochastic root?
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A*******s 发帖数: 3942 | 9 thanks a lot. but i don't think this solution guarantees a stochastic root,
but ur reference is helpful.
【在 L*******t 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 补充一下,如果你的i是偶数,可以用sqrtm函数get the root in a recursive way. : sqrtm是MATLAB函数
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d********t 发帖数: 9628 | 10 啥叫root matrix
1
【在 A*******s 的大作中提到】![](/moin_static193/solenoid/img/up.png) : root matrix that has the stochastic (transition) matrix property (row sum=1 : and non negative real elements)
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A*******s 发帖数: 3942 | 11 if B^i=A, , B and A are both square matrix, B is A's i-th root matrix
【在 d********t 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 啥叫root matrix : : 1
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d********t 发帖数: 9628 | 12 以前数学课没学过啊。
【在 A*******s 的大作中提到】![](/moin_static193/solenoid/img/up.png) : if B^i=A, , B and A are both square matrix, B is A's i-th root matrix
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c******0 发帖数: 59 | 13 Well normally when you consider a matrix, the ith root of it is done by:
diagonalize the matrix, into P'AP, where 'means inverse
then you take the ith root of its eigenvalues, say A becomes B
Now the ith root of Matrix is P'BP. This is because P'P = I
I assume the approach is gonna be similar to this problem |
A*******s 发帖数: 3942 | 14 not that trivial, think about complex eigen values
【在 c******0 的大作中提到】![](/moin_static193/solenoid/img/up.png) : Well normally when you consider a matrix, the ith root of it is done by: : diagonalize the matrix, into P'AP, where 'means inverse : then you take the ith root of its eigenvalues, say A becomes B : Now the ith root of Matrix is P'BP. This is because P'P = I : I assume the approach is gonna be similar to this problem
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