Empty Matrices

A matrix may have one or both dimensions zero and operations on empty matrices are handled as described by Carl de Boor in An Empty Exercise SIGNUM, Volume 25, pages 2-6, 1990 and C. N. Nett and W. M. Haddad in A System-Theoretic Appropriate Realization of the Empty Matrix Concept IEEE Transactions on Automatic Control, Volume 38, Number 5 May 1993. Briefly given a scalar s, an m by n matrix M(mxn) and an m by n empty matrix [](mxn) (with either one or both dimensions equal to zero) the following are true:

     s * [](mxn) = [](mxn) * s = [](mxn)
     
         [](mxn) + [](mxn) = [](mxn)
     
         [](0xm) *  M(mxn) = [](0xn)
     
          M(mxn) * [](nx0) = [](mx0)
     
         [](mx0) * [](0xn) =  0(mxn)
     

By default dimensions of the empty matrix are printed along with the empty matrix symbol []. The built-in variable print_empty_dimensions controls this behavior.

print_empty_dimensions

Built-in Variable

If the value of print_empty_dimensions is nonzero the dimensions of empty matrices are printed along with the empty matrix symbol []. For example, the expression zeros (3 0) will print ans = [](3x0)

Empty matrices may also be used in assignment statements as a convenient way to delete rows or columns of matrices. See Assignment Expressions.

warn_empty_list_elements

Built-in Variable

If the value of warn_empty_list_elements is nonzero print a warning when an empty matrix is found in a matrix list. For example a = [1 [], 3, [], 5] The default value is 0.

When Octave parses a matrix expression it examines the elements of the list to determine whether they are all constants. If they are it replaces the list with a single matrix constant.