On matrices with positive inverses
نویسندگان
چکیده
منابع مشابه
Persistently positive inverses of perturbed M-matrices
A well known property of anM-matrixA is that the inverse is element-wise non-negative, which we write asA−1 0. In this paper we consider perturbations ofM-matrices and obtain bounds on the perturbations so that the non-negative inverse persists. The bounds are written in terms of decay estimates which characterize the decay (along rows) of the elements of the inverse matrix. We obtain results f...
متن کاملInverses of symmetric, diagonally dominant positive matrices and applications
We prove tight bounds for the ∞-norm of the inverse of a symmetric, diagonally dominant positive matrix J ; in particular, we show that ‖J‖∞ is uniquely maximized among all such J . We also prove a new lower-bound form of Hadamard’s inequality for the determinant of diagonally dominant positive matrices and an improved upper bound for diagonally balanced positive matrices. Applications of our r...
متن کاملStructured matrices and inverses
A matrix (and any associated linear system) will be referred to as structured if it has a small displacement rank. It is known that the inverse of a structured matrix is structured, which allows fast inversion (or solution), and reduced storage requirements. According to two definitions of displacement structure of practical interest, it is shown here that several types of inverses are also str...
متن کاملOn generalized inverses of banded matrices
Bounds for the ranks of upper-right submatrices of a generalized inverse of a strictly lower k-banded matrix are obtained. It is shown that such ranks can be exactly predicted under some conditions. The proof uses the Nullity Theorem and bordering technique for generalized inverse.
متن کاملFast transforms: Banded matrices with banded inverses.
It is unusual for both A and A(-1) to be banded--but this can be a valuable property in applications. Block-diagonal matrices F are the simplest examples; wavelet transforms are more subtle. We show that every example can be factored into A = F(1)...F(N) where N is controlled by the bandwidths of A and A(-1) (but not by their size, so this extends to infinite matrices and leads to new matrix gr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applicationes Mathematicae
سال: 1963
ISSN: 1233-7234,1730-6280
DOI: 10.4064/am-7-2-164-169