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Distances In Weighted Trees And Group Inverse Of Laplacian Matrices, S. J. Kirkland, M. Neumann, Bryan L. Shader
Distances In Weighted Trees And Group Inverse Of Laplacian Matrices, S. J. Kirkland, M. Neumann, Bryan L. Shader
Bryan L Shader
In this paper we find formulas for group inverses of Laplacians of weighted trees. We then develop a relationship between entries of the group inverse and various distance functions on trees. In particular, we show that the maximal and minimal entries on the diagonal of the group inverse correspond to certain pendant vertices of the tree and to a centroid of the tree, respectively. We also give a characterization for the group inverses of the Laplacian of an unweighted tree to be an M-matrix.
On Matrices With Signed Null Spaces, S. J. Kim, Bryan L. Shader, S. G. Hwang
On Matrices With Signed Null Spaces, S. J. Kim, Bryan L. Shader, S. G. Hwang
Bryan L Shader
We denote by Q(A) the set of all matrices with the same sign pattern as A. A matrix A has signed null-space provided there exists a set S of sign patterns such that the set of sign patterns of vectors in the null-space of (A) over tilde is S for each (A) over tilde is an element of Q (A). Some properties of matrices with signed null-spaces are investigated.
A Simple Proof Of Fiedler's Conjecture Concerning Orthogonal Matrices, Bryan L. Shader
A Simple Proof Of Fiedler's Conjecture Concerning Orthogonal Matrices, Bryan L. Shader
Bryan L Shader
We give a simple proof that an n x n orthogonal matrix with n greater than or equal to 2 which cannot be written as a direct sum has at least 4n - 4 nonzero entries.
Sign Patterns That Allow A Positive Or Nonnegative Left Inverse, I. J. Kim, D. D. Olesky, Bryan L. Shader, P. Van Den Driessche
Sign Patterns That Allow A Positive Or Nonnegative Left Inverse, I. J. Kim, D. D. Olesky, Bryan L. Shader, P. Van Den Driessche
Bryan L Shader
An m by n sign pattern S is an m by n matrix with entries in {+,-, 0}. Such a sign pattern allows a positive (resp., nonnegative) left inverse, provided that there exist an m by n matrix A with the sign pattern S and an n by m matrix B with only positive ( resp., nonnegative) entries satisfying BA = I-n, where I-n is the n by n identity matrix. For m > n >= 2, a characterization of m by n sign patterns with no rows of zeros that allow a positive left inverse is given. This leads to …
Distances In Weighted Trees And Group Inverse Of Laplacian Matrices, S. J. Kirkland, M. Neumann, Bryan L. Shader
Distances In Weighted Trees And Group Inverse Of Laplacian Matrices, S. J. Kirkland, M. Neumann, Bryan L. Shader
Bryan L Shader
In this paper we find formulas for group inverses of Laplacians of weighted trees. We then develop a relationship between entries of the group inverse and various distance functions on trees. In particular, we show that the maximal and minimal entries on the diagonal of the group inverse correspond to certain pendant vertices of the tree and to a centroid of the tree, respectively. We also give a characterization for the group inverses of the Laplacian of an unweighted tree to be an M-matrix.
A Simple Proof Of Fiedler's Conjecture Concerning Orthogonal Matrices, Bryan L. Shader
A Simple Proof Of Fiedler's Conjecture Concerning Orthogonal Matrices, Bryan L. Shader
Bryan L Shader
We give a simple proof that an n x n orthogonal matrix with n greater than or equal to 2 which cannot be written as a direct sum has at least 4n - 4 nonzero entries.
Sign Patterns That Allow A Positive Or Nonnegative Left Inverse, I. J. Kim, D. D. Olesky, Bryan L. Shader, P. Van Den Driessche
Sign Patterns That Allow A Positive Or Nonnegative Left Inverse, I. J. Kim, D. D. Olesky, Bryan L. Shader, P. Van Den Driessche
Bryan L Shader
An m by n sign pattern S is an m by n matrix with entries in {+,-, 0}. Such a sign pattern allows a positive (resp., nonnegative) left inverse, provided that there exist an m by n matrix A with the sign pattern S and an n by m matrix B with only positive ( resp., nonnegative) entries satisfying BA = I-n, where I-n is the n by n identity matrix. For m > n >= 2, a characterization of m by n sign patterns with no rows of zeros that allow a positive left inverse is given. This leads to …