Empty Matrices - GNU Octave
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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.