On the existence of unimodular matrices with a prescribed submatrix
نویسندگان
چکیده
منابع مشابه
Existence of Matrices with Prescribed Off-Diagonal Block Element Sums
Necessary and sufficient conditions are proven for the existence of a square matrix, over an arbitrary field, such that for every principal submatrix the sum of the elements in the row complement of the submatrix is prescribed. The problem is solved in the cases where the positions of the nonzero elements of A are contained in a given set of positions, and where there is no restriction on the p...
متن کاملOn the discrepancy of strongly unimodular matrices
A (0, 1) matrix A is strongly unimodular if A is totally unimodular and every matrix obtained from A by setting a nonzero entry to 0 is also totally unimodular. Here we consider the linear discrepancy of strongly unimodular matrices. It was proved by Lováz, et.al. [5] that for any matrix A, lindisc(A) ≤ herdisc(A). (1) When A is the incidence matrix of a set-system, a stronger inequality holds:...
متن کاملThe Inverse Problem of Centrosymmetric Matrices with a Submatrix Constraint
By using Moore-Penrose generalized inverse and the general singular value decomposition of matrices, this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the centrosymmetric solutions with a submatrix constraint of matrix inverse problem AX = B. In addition, in the solution set of corresponding problem, the expression of the optimal approxi...
متن کاملOn the Existence of Sequences and Matrices With Prescribed Partial Sums of Elements
We prove necessary and sufficient conditions for the existence of sequences and matrices with elements in given intervals and with prescribed lower and upper bounds on the element sums corresponding to the sets of an orthogonal pair of partitions. We use these conditions to generalize known results on the existence of nonnegative matrices with a given zero pattern and prescribed row and column ...
متن کاملOn the Existence of Matrices with Prescribed Height and Level Characteristics
We detennine all possible relationa between the height (Weyr) characteristic and the level characteristic of an M-matrix. Under the assumption that the two characteristics have the same number of elements, we detennine the possible relations between the two characteristics for a wider class of matrices, which also contains the class of strictly triangular matrices over an arbitrary field. Given...
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: Linear Algebra and its Applications
سال: 2017
ISSN: 0024-3795
DOI: 10.1016/j.laa.2016.11.015