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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Spectral Properties Of A Sequence Of Matrices Connected To Each Other Via Schur Complement And Arising In A Compartmental Model, Evan Haskell, Vehbi Emrah Paksoy
Spectral Properties Of A Sequence Of Matrices Connected To Each Other Via Schur Complement And Arising In A Compartmental Model, Evan Haskell, Vehbi Emrah Paksoy
Mathematics Faculty Articles
We consider a sequence of real matrices An which is characterized by the rule that An−1 is the Schur complement in An of the (1,1) entry of An, namely −en, where en is a positive real number. This sequence is closely related to linear compartmental ordinary differential equations. We study the spectrum of An. In particular,we show that An has a unique positive eigenvalue λn and {λn} is a decreasing convergent sequence. We also study the stability of An for small n using the Routh-Hurwitz criterion.
On The Null Space Structure Associated With Trees And Cycles, Shaun M. Fallat, Shahla Nasserasr
On The Null Space Structure Associated With Trees And Cycles, Shaun M. Fallat, Shahla Nasserasr
Mathematics Faculty Articles
In this work, we study the structure of the null spaces of matrices associated with graphs. Our primary tool is utilizing Schur complements based on certain collections of independent vertices. This idea is applied in the case of trees, and seems to represent a unifying theory within the context of the support of the null space. We extend this idea and apply it to describe the null vectors and corresponding nullities of certain symmetric matrices associated with cycles
Hua's Matrix Equality And Schur Complements, Chris Paige, George P. H. Styan, Bo-Ying Wang, Fuzhen Zhang
Hua's Matrix Equality And Schur Complements, Chris Paige, George P. H. Styan, Bo-Ying Wang, Fuzhen Zhang
Mathematics Faculty Articles
The purpose of this paper is to revisit Hua's matrix equality (and inequality) through the Schur complement. We present Hua's original proof and two new proofs with some extensions of Hua's matrix equality and inequalities. The new proofs use a result concerning Shur complements and a generalization of Sylvester's law of inertia, each of which is useful in its own right.
Disc Separation Of The Schur Complement Of Diagonally Dominant Matrices And Determinantal Bounds, Jianzhou Liu, Fuzhen Zhang
Disc Separation Of The Schur Complement Of Diagonally Dominant Matrices And Determinantal Bounds, Jianzhou Liu, Fuzhen Zhang
Mathematics Faculty Articles
We consider the Gersgorin disc separation from the origin for (doubly) diagonally dominant matrices and their Schur complements, showing that the separation of the Schur complement of a (doubly) diagonally dominant matrix is greater than that of the original grand matrix. As application we discuss the localization of eigenvalues and present some upper and lower bounds for the determinant of diagonally dominant matrices.