Strassen Formulas

Author

Eric W. Weisstein
February 5, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Algebra/StrassenFormulas.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/StrassenFormulas.html.

©2006 Wolfram Research, Inc. except for portions noted otherwise

Check

StrassenProduct[a_,b_]:=Module[
{
Q1=(a[[1,1]]+a[[2,2]])(b[[1,1]]+b[[2,2]]),
Q2=(a[[2,1]]+a[[2,2]])b[[1,1]],
Q3=a[[1,1]](b[[1,2]]-b[[2,2]]),
Q4=a[[2,2]](-b[[1,1]]+b[[2,1]]),
Q5=(a[[1,1]]+a[[1,2]])b[[2,2]],
Q6=(-a[[1,1]]+a[[2,1]])(b[[1,1]]+b[[1,2]]),
Q7=(a[[1,2]]-a[[2,2]])(b[[2,1]]+b[[2,2]])
},
{{Q1+Q4-Q5+Q7,Q3+Q5},{Q2+Q4,Q1+Q3-Q2+Q6}}
]

StrassenProduct[(({{(Subscript[a, 11]), (Subscript[a, 12])}, {(Subscript[a, 21]), (Subscript[a, 22])}})),(({{(Subscript[b, 11]), (Subscript[b, 12])}, {(Subscript[b, 21]), (Subscript[b, 22])}}))]//Simplify//TraditionalForm

(({{(Subscript[a, 11]), (Subscript[a, 12])}, {(Subscript[a, 21]), (Subscript[a, 22])}})).(({{(Subscript[b, 11]), (Subscript[b, 12])}, {(Subscript[b, 21]), (Subscript[b, 22])}}))//TraditionalForm