- #1
PoomjaiN
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Dear Friends & Colleagues,
I have a couple of nagging issues with mathematics I was hoping anyone of you would kindly be able to help resolve.
Given a few (let’s say 3) square matrices, A_1, A_2, A_3, and the corresponding principal eigenvector (eigenvector corresponding to the largest eigenvalue, as per eigenvalue decomposition) designated v_1, v_2, v_3. Define the aggregate matrix, A_0, and its corresponding principal eigenvector v_0
I wish to know (i) under which conditions would it be possible to guarantee that there exists a set of weights, w_1, w_2, w_3, such that w_1*v_1 + w_2*v_2 + w_3*v_3 = v_0 (which I am tempted to define as ‘sub-additivity’ vis-à-vis said principal eigenvectors), and (ii) whether an algorithm exists to find these weights, even for a severely restricted case.
Any enlightenment on this issue would be most truly appreciated.
Yours sincerely,
Poomjai Nacaskul (Ph.D.)
I have a couple of nagging issues with mathematics I was hoping anyone of you would kindly be able to help resolve.
Given a few (let’s say 3) square matrices, A_1, A_2, A_3, and the corresponding principal eigenvector (eigenvector corresponding to the largest eigenvalue, as per eigenvalue decomposition) designated v_1, v_2, v_3. Define the aggregate matrix, A_0, and its corresponding principal eigenvector v_0
I wish to know (i) under which conditions would it be possible to guarantee that there exists a set of weights, w_1, w_2, w_3, such that w_1*v_1 + w_2*v_2 + w_3*v_3 = v_0 (which I am tempted to define as ‘sub-additivity’ vis-à-vis said principal eigenvectors), and (ii) whether an algorithm exists to find these weights, even for a severely restricted case.
Any enlightenment on this issue would be most truly appreciated.
Yours sincerely,
Poomjai Nacaskul (Ph.D.)