Up: Matrices

4.1.1 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.

— Built-in Function: val = print_empty_dimensions ()
— Built-in Function: old_val = print_empty_dimensions (new_val)
— Built-in Function: print_empty_dimensions (new_val, "local")

Query or set the internal variable that controls whether the dimensions of empty matrices are printed along with the empty matrix symbol, ‘[]’. For example, the expression 

          zeros (3, 0)

will print 

          ans = [](3x0)

When called from inside a function with the "local" option, the variable is changed locally for the function and any subroutines it calls. The original variable value is restored when exiting the function.

See also: format.

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

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.