Hollow matrix

In mathematics, a hollow matrix may refer to one of several related classes of matrix.
Definitions.
Sparse.
A "hollow matrix" may be one with "few" non-zero entries: that is, a sparse matrix.
Diagonal entries all zero.
A "hollow matrix" may be a square matrix whose diagonal elements are all equal to zero. That is, an "n" × "n" matrix "A" = ("a""ij") is hollow if "a""ij" = 0 whenever "i" = "j" (i.e. "a""ii" = 0 for all "i"). The most obvious example is the real skew-symmetric matrix. Other examples are the adjacency matrix of a finite simple graph; a distance matrix or Euclidean distance matrix.
In other words, any square matrix that takes the form
is a hollow matrix, where the symbol formula_2 denotes an arbitrary entry.
For example,
is a hollow matrix.
Block of zeroes.
A "hollow matrix" may be a square "n" × "n" matrix with an "r" × "s" block of zeroes where "r" + "s" > "n".