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: 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.