(octave.info)Empty Matrices

---

Up: Matrices

---

Enter node , (file) or (file)node

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.

 -- : VAL = print_empty_dimensions ()
 -- : OLD_VAL = print_empty_dimensions (NEW_VAL)
 -- : 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: Note: format.

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