Node:Empty Matrices, Up: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.