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POSITIVE EIGENVALUES FOR MATRIX DIFFERENCE EQUATIONS
"... ABSTRACT. We consider a selfadjoint matrix difference eigenvalue problem with Dirichlet or antiperiodic boundary conditions. By reformulation of the problem as a Stieltjes Sturm–Liouville equation and then applying recent inequalities developed by Brown, Clark, and Hinton, conditions are given whi ..."
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which imply all eigenvalues are positive of the difference equation problem. Examples are given which illustrate how these conditions allow cancellation of the positive and negative parts of the coefficients in the difference equation to preserve the positivity of the eigenvalues. AMS (MOS) Subject
ON SYMMETRIC MATRICES WITH EXACTLY ONE POSITIVE EIGENVALUE ∗
"... Abstract. We present a class of nonsingular matrices, the MC ′matrices, and prove that the class of symmetric MCmatrices introduced by Shen, Huang and Jing [On inclusion and exclusion intervals for the real eigenvalues of real matrices. SIAM J. Matrix Anal. Appl., 31:816830, 2009] and the class o ..."
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of symmetric MC ′matrices are both subsets of the class of symmetric matrices with exactly one positive eigenvalue. Some other sufficient conditions for a symmetric matrix to have exactly one positive eigenvalue are derived.
SignPatterns Which Require A Positive Eigenvalue
, 2000
"... We investigate matrices which have a positive eigenvalue by virtue of their sign–pattern and regardless of the magnitudes of the entries. When all the off–diagonal entries are nonzero, we show that an n × n sign–pattern, n = 3, 4, requires a positive eigenvalue if and only if it has at least one no ..."
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Cited by 3 (0 self)
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We investigate matrices which have a positive eigenvalue by virtue of their sign–pattern and regardless of the magnitudes of the entries. When all the off–diagonal entries are nonzero, we show that an n × n sign–pattern, n = 3, 4, requires a positive eigenvalue if and only if it has at least one
Existence and uniqueness of positive eigenvalues for certain eigenvalue system
 System Science and Mathematical Science
"... In this paper we consider certain eigenvalue systems. Imposing some reasonable hypotheses, we prove that the eigenvalue systems have a unique eigenvalue with positive eigenfunctions, and that the eigenfunction is unique up to a scalar multiple. Key words and phrases: eigenvalue problem; eigenfunctio ..."
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Cited by 1 (1 self)
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In this paper we consider certain eigenvalue systems. Imposing some reasonable hypotheses, we prove that the eigenvalue systems have a unique eigenvalue with positive eigenfunctions, and that the eigenfunction is unique up to a scalar multiple. Key words and phrases: eigenvalue problem
Geometric conditions for the existence of positive eigenvalues of matrices
 Lin. Alg. Appl. (Leiters
, 1981
"... Finitedimensional theorems of PerronFrobenius type are proved. For A E e nn and a nonnegative integer k. we let w/t(A) be the cone generated by AI:, Ak+l.... in en". We show that A satisfies the PerronSchaefer condition if and only if the closure wk(A) of w/t(A) is a pointed cone. This theor ..."
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Cited by 7 (2 self)
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. This theorem is closely related to several known results. If k> po ( A). the index of the eigenvalue 0 in spec A. we prove that A has a positive eigenvalue if and only if w/t(A) is a pointed nonzero cone or. equivalently w/t(A) is not a real subspace of en". Our proofs are elementary and based on a
ELA POSITIVE EIGENVALUES AND TWOLETTER GENERALIZED WORDS ∗
"... Abstract. A generalized word in two letters A and B is an expression of the form W = Aα1B β1 Aα2 Bβ2 ···AαN BβN in which the exponents are nonzero real numbers. When independent positive definite matrices are substituted for A and B, it is of interest whether W necessarily has positive eigenvalues. ..."
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Abstract. A generalized word in two letters A and B is an expression of the form W = Aα1B β1 Aα2 Bβ2 ···AαN BβN in which the exponents are nonzero real numbers. When independent positive definite matrices are substituted for A and B, it is of interest whether W necessarily has positive eigenvalues
Positive eigenvalues of generalized words in two Hermitian positive definite matrices
 Novel Approaches to Hard Discrete Optimization, volume 37 of Fields Institute Communications
, 2003
"... Abstract. We define a word in two positive definite (complex Hermitian) matrices A and B as a finite product of real powers of A and B. The question of which words have only positive eigenvalues is addressed. This question was raised some time ago in connection with a longstanding problem in theore ..."
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Cited by 9 (5 self)
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Abstract. We define a word in two positive definite (complex Hermitian) matrices A and B as a finite product of real powers of A and B. The question of which words have only positive eigenvalues is addressed. This question was raised some time ago in connection with a longstanding problem
On positive eigenvalues of onebody Schrodinger operators
 Commun. Pure Appl. Math
, 1969
"... The last twenty years have produced a rather extensive literature on the exact mathematical treatment of general features of the Schrodinger equation for one or many particles. One of the more intriguing questions concerns the presence of discrete eigenvalues of positive energy (that is squareinteg ..."
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Cited by 2 (1 self)
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The last twenty years have produced a rather extensive literature on the exact mathematical treatment of general features of the Schrodinger equation for one or many particles. One of the more intriguing questions concerns the presence of discrete eigenvalues of positive energy (that is squareintegrable
Positive eigenvalues and twoletter generalized words
 Electronic Journal of Linear Algebra
"... Abstract. A generalized word in two letters A and B is an expression of the form W = ..."
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Cited by 8 (6 self)
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Abstract. A generalized word in two letters A and B is an expression of the form W =
Results 1  10
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