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Noncentral, nonsingular matrix variate beta distribution
 BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS (2007), 21, PP. 175–186
, 2007
"... In this paper, we determine the density of a nonsingular noncentral matrix variate beta type I and II distributions under different definitions. ..."
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Cited by 3 (3 self)
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In this paper, we determine the density of a nonsingular noncentral matrix variate beta type I and II distributions under different definitions.
On GelfandNaimark decomposition of a nonsingular matrix
"... Abstract. Let F = C or R and A ∈ GLn(F). Let s(A) ∈ R n + be the singular values of A, λ(A) ∈ C n the unordered ntuple of eigenvalues of A, a(A): = diag R ∈ R n +, where A = QR is the QR decomposition of A, u(A): = diag U ∈ C n, where A = LωU is any GelfandNaimark decomposition. We obtain comple ..."
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Cited by 2 (1 self)
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Abstract. Let F = C or R and A ∈ GLn(F). Let s(A) ∈ R n + be the singular values of A, λ(A) ∈ C n the unordered ntuple of eigenvalues of A, a(A): = diag R ∈ R n +, where A = QR is the QR decomposition of A, u(A): = diag U ∈ C n, where A = LωU is any GelfandNaimark decomposition. We obtain complete relations between (1) u(A) and a(A), (2) u(A) and s(A), (3) u(A) and λ(A), and (4) a(A) and λ(A). We also study the relations between any three elements among u, λ, a, s. 1.
LDU FACTORIZATION OF NONSINGULAR TOTALLY NONPOSITIVE MATRICES ∗
"... Abstract. An n × n real matrix A is said to be (totally negative) totally nonpositive if every minor is (negative) nonpositive. In this paper, we study the properties of a totally nonpositive matrix and characterize the case of a nonsingular totally nonpositive matrix A with a11 < 0 in terms of i ..."
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Cited by 1 (1 self)
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Abstract. An n × n real matrix A is said to be (totally negative) totally nonpositive if every minor is (negative) nonpositive. In this paper, we study the properties of a totally nonpositive matrix and characterize the case of a nonsingular totally nonpositive matrix A with a11 < 0 in terms
ASTABLETESTTOCHECKIFAMATRIX IS A NONSINGULAR MMATRIX
"... Abstract. A stable test for checking if a matrix is a nonsingular Mmatrix is presented. Its computational cost is, in the worst case, O(n 2)elementary operations higher than the computational cost of Gaussian elimination. The test can be applied to check if a nonnegative matrix has spectral radius ..."
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Abstract. A stable test for checking if a matrix is a nonsingular Mmatrix is presented. Its computational cost is, in the worst case, O(n 2)elementary operations higher than the computational cost of Gaussian elimination. The test can be applied to check if a nonnegative matrix has spectral radius
A Singular Loop Transformation Framework Based on Nonsingular Matrices
, 1992
"... In this paper, we discuss a loop transformation framework that is based on integer nonsingular matrices. The transformations included in this framework are called transformations and include permutation, skewing and reversal, as well as a transformation called loop scaling. This framework is mo ..."
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Cited by 130 (8 self)
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In this paper, we discuss a loop transformation framework that is based on integer nonsingular matrices. The transformations included in this framework are called transformations and include permutation, skewing and reversal, as well as a transformation called loop scaling. This framework
Efficient Generation of Random Nonsingular Matrices
 Random Structures Algorithms
, 1993
"... We present an efficient algorithm for generating an n \Theta n nonsingular matrix uniformly over a finite field. This algorithm is useful for several cryptographic and checking applications. Over GF[2] our algorithm runs in expected time M(n) + O(n 2 ), where M(n) is the time needed to multiply t ..."
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Cited by 5 (0 self)
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We present an efficient algorithm for generating an n \Theta n nonsingular matrix uniformly over a finite field. This algorithm is useful for several cryptographic and checking applications. Over GF[2] our algorithm runs in expected time M(n) + O(n 2 ), where M(n) is the time needed to multiply
Currents twisting and nonsingular matrices
"... Abstract. We show that for k ≥ 3, given any matrix in GL(k, Z), there is a hyperbolic fully irreducible automorphism of the free group of rank k whose induced action on Z k is the given matrix. 1. ..."
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Cited by 8 (0 self)
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Abstract. We show that for k ≥ 3, given any matrix in GL(k, Z), there is a hyperbolic fully irreducible automorphism of the free group of rank k whose induced action on Z k is the given matrix. 1.
On singular and nonsingular Hmatrices
"... Let denote by M(A) the comparison matrix of a square Hmatrix A, that is, M(A) is an Mmatrix. Hmatrices such that M(A) is nonsingular are well studied in the literature. In this work, we study some characterizations of singular and nonsingular Hmatrices when M(A) is singular. The spectral radius ..."
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Let denote by M(A) the comparison matrix of a square Hmatrix A, that is, M(A) is an Mmatrix. Hmatrices such that M(A) is nonsingular are well studied in the literature. In this work, we study some characterizations of singular and nonsingular Hmatrices when M(A) is singular. The spectral radius
Criteria for nonsingular Hmatrices
"... Abstract—Nonsingular H − matrices play a very important role in matrix analysis and numerical algebra. Based on the concept and properties of the generalized strictly diagonal dominance matrices, we partition the row and column index set of square matrix, construct a positive diagonal matrix accordi ..."
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Abstract—Nonsingular H − matrices play a very important role in matrix analysis and numerical algebra. Based on the concept and properties of the generalized strictly diagonal dominance matrices, we partition the row and column index set of square matrix, construct a positive diagonal matrix
Ray Patterns of Matrices and Nonsingularity
"... A complex matrix A is raynonsingular if det(X ffi A) 6= 0 for every matrix X with positive entries. A sufficient condition for raynonsingularity is that the origin is not in the relative interior of the convex hull of the signed transversal products of A. The concept of an isolated set of trans ..."
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A complex matrix A is raynonsingular if det(X ffi A) 6= 0 for every matrix X with positive entries. A sufficient condition for raynonsingularity is that the origin is not in the relative interior of the convex hull of the signed transversal products of A. The concept of an isolated set
Results 1  10
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775