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Boosted by jsonstein@masto.deoan.org ("Jeff Sonstein"):
johncarlosbaez@mathstodon.xyz ("John Carlos Baez") wrote:
RE: https://mathstodon.xyz/@robinhouston/115821134807127928
Wow, someone discovered a more efficient way of multiplying two 3×3 matrices! You might think this would have already been solved.
This new method, due to A. Perminov, uses 23 multiplications and 58 addition/subtractions. The previous best used 60 addition/subtractions and 23 multiplications - and this was discovered only in August last year. The first scheme using 23 multiplications dates back to 1976.
This is not at all the sort of math I'd ever want to work on; it reminds me of pole-vaulting and other specialized athletic competitions. But it's one of those problems that's easy to explain, hard to solve.
(As @robinhouston emphasizes, this new scheme is the only the best known if you want to allow for the possibility that multiplication could be noncommutative for the 'numbers' in your matrices - like for the quaternions. For commutative rings, like the reals and complex numbers, people already know how to do multiply 3×3 matrices with just 21 multiplications.)