My Math Forum Inverse Matrix problem

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 September 12th, 2012, 12:30 PM #1 Newbie   Joined: Apr 2012 Posts: 2 Thanks: 0 Inverse Matrix problem Hello, To explain my problem, I will begin with direct problem : We suppose to calculate a product of n matrix like : $T= \begin{pmatrix} T_1_1&T_1_2 \\ T_2_1&T_2_2 \end{pmatrix}= a_1*a_2*...*a_n \begin{pmatrix}exp(i*C1*d1)&b_1*exp(-i*C_1*d_1)\\b_1*exp(i*C_1*d_1)&exp(-i*C_1*d_1) \end{pmatrix} * \begin{pmatrix} exp(i*C1*d_2)&b_2*exp(-i*C_1*d_2)\\b_2*exp(i*C_1*d_2)&exp(-i*C_1*d_2)\end{pmatrix} *...* \begin{pmatrix}exp(i*C_1*d_n)&b_n*exp(-i*C_1*d_n)\\b_n*exp(i*C_1*d_n)&exp(-i*C_1*d_n)\end{pmatrix}$For direct problem ( it does not concern me)we don't know the elements of the matrix T, and we know $a_1, a_2,.. ; b_1, b_2,...; C1 ; d_1, d_2,...$ For inverse problem we know the elements of the matrix T related to every $C_1, C_2,... C_n$ and we know also $a_1, a_2,.. ; b_1, b_2,...$ ; but we don't know $d_1, d_2,...$ This is my problem, I want to know if we can solve it analytically (and we get $d_1, d_2,... d_n$ ) or if there is a dedicated algorithm to solve this kind of nonlinear inverse problems thanks
 September 13th, 2012, 06:08 AM #2 Senior Member   Joined: Aug 2012 Posts: 229 Thanks: 3 Re: Inverse Matrix problem Hey soft001. Does this problem only involve 2x2 matrices? If so, the best suggestion is to see if you can get a form for individual elements of your final matrix since the inverse for a 2x2 matrix is extremely straight-forward. I was going to say if these were rotation or special unitary that you could simply compose rotations to get a formula for the final rotation matrix in terms of a polar decomposition but I don't think this will hold in general.

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