I am a bit confused with this wikipedia article, hoping someone can clarify it. Looking at the Strassen algorithm page it is clear that this is an algorithm for reducing multiplication operations.
Why is a matrix multiplication algorithm touted as a matrix inversion algorithm? last time i checked it was totally odd to apply Gauss-Jordan elimination to multiply matrices
thanks
Best Answer
Gauss Jordan algorithm is effecting manipulations on the lines of the matrix to invert. Each operation is equivalent to multiply your matrix on the left side by a matrix of the form $I_n +\lambda E_{ij}$ where $E_{ij}$ is an elementary matrix: $E_{ij}=(e^{ij}_{kl})_{1\leq k,l\leq n}$ where $e^{ij}_{kl}=1$ if $k=i$ and $l=j$, and $0$ otherwise.
So each time you are making such an operation, you are actually multiplying your matrix by some other matrix, so all your line operations are actually equivalent to multiply your matrix by a series of matrix of the form $I_n +\lambda E_{ij}$.
HTH