Stieltjes matrix

Stieltjes matrix

In mathematics, particularly matrix theory, a Stieltjes matrix is a real symmetric positive definite matrix with nonpositive off-diagonal entries. A Stieltjes matrix is necessarily an M-matrix. Every "n×n" Stieltjes matrix is invertible to a nonsingular symmetric matrix with nonnegative entries, though the converse of this statement is not true in general for "n > 2".

From the above definition, a Stieltjes matrix is a symmetric invertible Z-matrix whose eigenvalues have positive real parts. As it is a Z-matrix, its off-diagonal entries are less than or equal to zero.

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