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CLASSIFICATION OF CRITICAL HERMITIAN MATRIX MODELS
Modern Physics Letters A, 1991The critical properties of Hermitian matrix models in the one-arc phase may be simply understood and completely classified by the behavior of the eigenvalue distribution at its ends. The most general critical behavior involves two scaling functions naturally associated with each end of the distribution, and two KdV-type string equations with differing
Dalley, Simon +2 more
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TACHYONIC HERMITIAN ONE-MATRIX MODELS
Modern Physics Letters A, 1991We treat the hermitian one-matrix model in the case where the quadratic term of the matrix potential has a negative coefficient (negative mass). In that case two scaling functions are necessary in the continuum limit. We analyze the problem both in the spherical and the double scaling limits.
Mathieu, Pierre, Sénéchal, David
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On Scaled Almost-Diagonal Hermitian Matrix Pairs
SIAM Journal on Matrix Analysis and Applications, 1997This paper contains estimates concerning the block structure of Hermitian matrices H and M, which make a scaled diagonally dominant definite pair. The obtained bounds are expressed in terms of relative gaps in the spectrum of the pair (H, M) and norms of certain blocks of the matrices DHD and DMD, where D is the square root of the inverse of the ...
Vjeran Hari, Zlatko Drmac
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Matrices Normal with Respect to an Hermitian Matrix
American Journal of Mathematics, 1938Verf. geht von der Bemerkung aus, daß \(A\) dann und nur dann im Schur-Toeplitzschen Sinne, normal (d. h. \(AA^* = A^*A\)) ist, wenn \(A^*\) eine Funktion (oder, da die Matrizen als endlich vorausgesetzt sind, ein Polynom) von \(A\) ist. Indem er die Einheitsmatrix \(E\) durch eine beliebige nichtsinguläre Hermitesche Matrix \(H\) ersetzt, definiert er
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Extremal ranks of matrix expression of A−BXC with respect to Hermitian matrix
Applied Mathematics and Computation, 2010The authors discuss the extremal ranks of matrix expression of \(A - BXC\) with respect to \(X^H = X\), by applying the quotient singular value decomposition and some rank equalities of matrices.
Wenbin Guo, Tingzhu Huang
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Calculation of the Eigenvalues of a Tridiagonal Hermitian Matrix
Journal of Mathematical Physics, 1961For real symmetric or Hermitian matrices with tridiagonal form, the secular equation may be written as a continued fraction equation f(λ)=0. f(λ) is a member of a recursively defined sequence R(n)(λ) of n continued fractions if the secular equation is of the nth order. The basis for a new method of computing the eigenvalues of such tridiagonal matrices
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Nilpotent matrix and Hermitian matrix
International Journal on Science and TechnologyNilpotent and Hermitian matrices are two important classes of matrices with distinct properties. A nilpotent matrix is a square matrix that, when raised to some power, becomes the zero matrix. A Hermitian matrix, on the other hand, is a square matrix that is equal to its conjugate transpose.
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Principal Submatrices of a Hermitian Matrix
Linear and Multilinear Algebra, 2003Suppose k 1 ,
Chi-Kwong Li, Yiu-Tung Poon
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Approximation by a Hermitian Positive Semidefinite Toeplitz Matrix
SIAM Journal on Matrix Analysis and Applications, 1993The authors study the problem of finding the closest Hermitian positive semidefinite Toeplitz matrix of a given rank to an arbitrary given matrix (in the Frobenius norm = Hilbert-Schmidt norm). They introduce two methods, one is based on using a special orthonormal basis in the space of Hermitian Toeplitz matrices and the second is a modified ...
T. J. Suffridge, Tom L. Hayden
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The minimal rank of with respect to Hermitian matrix
Applied Mathematics and Computation, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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