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.A hollow matrix may be a square matrix whose diagonal elements are all equal to zero. 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.
If A is an n×n hollow matrix, then the elements of A are given by
In other words, any square matrix that takes the form
is a hollow matrix.
For example:
is a hollow matrix.Properties
A hollow matrix may be a square n×n matrix with an r×s block of zeroes where r+s>n.
