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For questions about construction and modification of matrices, objects represented by 2-dimensional arrays that are used to define linear operators within linear algebra.

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Can you multiply complex 2x2 matrices in fewer than 21 real multiplies?

It is well known that 2x2 matrices can be multiplied using just 7 (instead of the obvious 8) multiplications in the ground field (Strassen-Winograd, etc.). … You can obviously combine these tricks, either way round, to multiply two complex 2x2 matrices using 21 real multiplies (and some additions etc.). Is it known whether you can do better? …
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