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 Variable: print_empty_dimensions

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.

— Built-in Variable: warn_empty_list_elements

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.