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If I gave you two 1025 x 1025 matrices, you wouldn't extend them to 2048 x 2048. … For non-square matrices: If you want to multiply a (100x100) by a (1000x100) matrix, that can be done trivially by calculating ten (100x100) x (100x100) products. …

What people often forget: They have a problem, and the have a sub problem that helps solving the problem. And then they try solving the (hard) sub problem - without realising there is a much better so …

You can take any matrix with N/2 < n < N rows and columns, pad it, and multiply it with Strassen's algorithm (or the naive algorithm for example), and then drop lots of zeroes that were created by the …

Ypu're starting from a completely wrong point. The execution time of matrix multiplication does not come from the number of multiplications and additions, it's the number of uncached memory accesses …

There is what you want to achieve, and there is reality, and sometimes they are in conflict. First you check if your problem is a special case that can be solved quicker, for example a sparse matrix. …

If we let $m = 2n^2$, that is the total number of elements in both matrices, then it is $m^{1.5} / 2^{1.5}$ multiplications and $m^{1.5} / 2^{1.5} - m/2$ additions. … are needed, depending on the shapes of the matrices. …

Hint: If the first row has k 1s, and the second row has k’ 1s, then there is no need to determine k’ at all if k’ <= k. How do you find in O(1) that k’ <= k? And if k’ > k, which you checked in O(1), …

Given these four results and the original M, you can calculate four of the matrices $M^6$ to $M^{25}$ in the same time again, provided the matrices are at most five powers apart from each other. … With these matrices calculated, all matrices up to $M^{108}$ and some more up to $M^{125}$ can be calculated in three times the time of a single matrix product if four processors are available. …

The question doesn't make any sense. It doesn't make sense to ask for the running time of a computation, unless you specify an algorithm for that computation. So how would you calculate this product? …

Interesting problem. Obviously with floating point involved, you can’t expect the same results, but we’d like to know what tended to give better results? In a completely unscientific way, you can per …