what is the matrix complexity when you multiply an mxn matrix by nxm matrix? my guess is that it will be m^2 since it would result to an m by m matrix, but im not too sure
all help would be much appreciated
2026-04-01 22:18:51.1775081931
What is the complexity when multiplying an mxn matrix by an nxm matrix?
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Computing the dot product of two length $n$ vectors requires $2n$ operations. In your case, you compute a dot product of two length $n$ vectors for each entry in the result. A total of $m^2 \cot 2n$ operations. The the operation count is $2m^2n$.
You can generalize this idea for an $n\times m$ matrix multiplied by a $m\times p$ matrix to get an operation count of $2mnp$