The discussion revolves around the properties of matrix multiplication, specifically addressing why the square of a sum of matrices does not equal the sum of their squares for all matrix sizes.
Participants are actively clarifying the expression and its components, with some guidance provided on the nature of matrix multiplication. Multiple interpretations of the expansion are being explored, indicating a productive discussion without a clear consensus yet.
There is an acknowledgment of the non-commutative property of matrix multiplication, which is central to the discussion. Participants also express uncertainty about specific terms in the matrix expansion.
Do you mean (e+f)2 = e2+fe+ef+f2? I might be misinterpreting it but I can't see where that extra "fe" came from and where the "f2" went.HallsofIvy said:(e+ f)^2= (e+f)(e+f)= e^2+ fe+ef+ fe. Remember that multiplication of matrices is not, in general, commutative!