Multiplication is not generally invertible. This is true of real numbers at zero and true of floating-point numbers at many non-zero values. For vectors and matrices, multiplication is highly non-invertible. Given this feature of reality, I'm not sure what else we can do.
On Sun, Apr 13, 2014 at 7:05 PM, <[email protected]> wrote: > Sure. This was just a side note. I would expect that a "notation" A*B/B > == A to be always true (except for division by zero of course), since > division the inverse process of multiplication, like for scalar values > (a*b/b == a or A.*B./B .== A). > > > Am Montag, 14. April 2014 00:38:57 UTC+2 schrieb andrew cooke: > >> >> >> On Sunday, 13 April 2014 19:18:31 UTC-3, [email protected] wrote: >>> >>> (Also note that division does not look like the inverse operation of >>> multiplication, since e.g. A=[1 2 3]; B=[1, 2, 4]; A*B/B == A returns >>> false.) >>> >> >> what would you expect to happen here? you're taking a scalar product and >> asking "this was one of the vectors; what is the other?". that's not well >> defined. you've lost information. >> >> on the other hand: >> >> julia> A = [1 2;3 4] >> 2x2 Array{Int64,2}: >> 1 2 >> 3 4 >> >> julia> B = [2 3;4 5] >> 2x2 Array{Int64,2}: >> 2 3 >> 4 5 >> >> julia> A*B/B >> 2x2 Array{Float64,2}: >> 1.0 2.0 >> 3.0 4.0 >> >> andrew >> >>
