Node:Empty Matrices, Up:Matrices



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.

print_empty_dimensions Built-in Variable
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.

warn_empty_list_elements Built-in Variable
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.