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Counting solutions to system of linear equations modulo prime
It's 2 raised to the power of size of null-space. The reason is that once you have a solution, adding any linear combination of vectors in null-space gives you a valid solution.
This problem comes ou …
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Estimating column sums of $A_1,\ A_1 A_2,\ A_1A_2A_3,\ \ldots$
Given $n\times n$ dense real valued matrices $A_1,\ldots, A_L$ let $P_i=A_1\ldots A_i$
For each $P_i$ I'm interested in obtaining the sum of all rows, and the sum of all columns.
Naive approach:
take …