Stieltjes matrix
In mathematics, particularly matrix theory, a Stieltjes matrix, named after Thomas Joannes Stieltjes, 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 nonnegative matrix, 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.
See also
References
- David M. Young (2003). Iterative Solution of Large Linear Systems. Dover Publications. p. 42. ISBN 0-486-42548-7.
- Anne Greenbaum (1987). Iterative Methods for Solving Linear Systems. SIAM. p. 162. ISBN 0-89871-396-X.
See what we do next...
OR
By submitting your email or phone number, you're giving mschf permission to send you email and/or recurring marketing texts. Data rates may apply. Text stop to cancel, help for help.
Success: You're subscribed now !