Definition:(0, 1)-Matrix/Examples

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Examples of (0, 1)-Matrix

Rook Matrix

An $8 \times 8$ (0, 1)-matrix in which:

at most one element in each row and column is $1$

is known as a rook matrix.


For example:

$\mathbf A = \begin{bmatrix} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{bmatrix}$


Not all rows and columns need have a $1$ in them.