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suppose we need to do some matrix calculation in recursion, how do we keep the matrix structure always same in each step of recursion? In particular, suppose there are 3*3 matrix $\begin{bmatrix}a11 & a12 & 0 \\ a21 & a22 & a23 \\ 0 & a31 & a32\end{bmatrix}$, what we need is to get the value of those elements of the matrix in some defined recursion algorithm, during the each step of the calculation, we need to keep this structure which means the top-right and bottom-left is always zero. But when we implement the recursion the value 0 would be changed in each step and the final matrix would be a full element matrix, could anyone tell me how to keep it? I suppose we need to give a indicator matrix and take the multiplication of two matrix? or other methods? Thanks a lot

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    What is the function, you want to get by recursion? Sparsity is not conserved with all matrix operations. Some are (LU of an bandwith-Matrix fo example) but others are not. Define what kind of function you want to evaluate, then we could heelp you. – 2017-01-17
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    Using EM algorithm to estimate the Kalman filter. Let's say for instance the simplest one $y_t = Ay_{t-1}$ continue to the 3*3 matrix, suppose y is 3*1 vector, A is the matrix I mentioned before. it's invertible matrix or generalized invertible matrix – 2017-01-17

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