Re: Multiplication of empty matrices?

[John W. Eaton]

On 06/09/2015 01:59 PM, Rik wrote:
> 6/9/15
>
> All,
>
> I came across this odd behavior for the multiplication of empty matrices:
>
> octave:1> x = zeros (0,1)
> x = [](0x1)
> octave:2> y = zeros (1,0)
> y = [](1x0)
> octave:3> x * y
> ans = [](0x0)
> octave:4> x .* y
> error: product: nonconformant arguments (op1 is 0x1, op2 is 1x0)
> octave:4> x * y'
> error: operator *: nonconformant arguments (op1 is 0x1, op2 is 0x1)
> magic(3) * x
> error: operator *: nonconformant arguments (op1 is 3x3, op2 is 0x1)
>
> Is this what Matlab does?  I would think that an empty matrix multiplying
> anything would return the empty matrix.

I think Octave is doing the right thing here.  Matlab should be doing 
the same now.  Originally, Matlab did not have dimensions for empty 
matrices (all empty matrices were just "empty") and operations on empty 
matrices usually returned empty matrices.  Octave originally behaved the 
same as Matlab.  Then I read Carl de Boor, An Empty Exercise, SIGNUM, 
Volume 25, pages 2-6, 1990 and C. N. Nett and W. M. Haddad, A System 
Theoretic Appropriate Realization of the Empty Matrix Concept, IEEE 
Transactions on Automatic Control, Volume 38, Number 5, May 1993 and 
realized that it's better to define operations that preserve the 
non-zero dimensions and always require dimensions to conform whether 
empty or not.  So I fixed Octave and eventually TMW did the same for Matlab.

jwe