In mathematics, a Hurwitz matrix, or Routh–Hurwitz matrix, in engineering stability matrix, is a structured real square matrix constructed with coefficients...
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mathematician Adolf Hurwitz independently proposed in 1895 to arrange the coefficients of the polynomial into a square matrix, called the Hurwitz matrix, and showed...
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Stable polynomial (section Hurwitz matrix)
square matrix A is called a Hurwitz matrix if every eigenvalue of A has strictly negative real part. Schur matrices is an analogue of the Hurwitz matrices...
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non-singular symmetric M-matrix is sometimes called a Stieltjes matrix. Hurwitz matrix P-matrix Perron–Frobenius theorem Z-matrix H-matrix Fujimoto, Takao &...
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theory, these are referred to as stoquastic operators. Hurwitz matrix M-matrix Metzler matrix P-matrix Bravyi, Sergey; DiVincenzo, David P.; Oliveira, Roberto...
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List of named matrices (redirect from List of matrix)
matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...
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, 1 , … , n {\displaystyle i=0,1,\ldots ,n} , are real. The square Hurwitz matrix associated to P is given below: H = ( a 1 a 3 a 5 … … … 0 0 0 a 0 a...
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differential equation M-matrix P-matrix Q-matrix, a specific kind of Metzler matrix Z-matrix Hurwitz matrix Stochastic matrix Positive systems Berman...
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Hurwitz matrix Hurwitz numbers Hurwitz polynomial Hurwitz problem Hurwitz quaternion order Hurwitz quaternion Hurwitz scheme Hurwitz surface Hurwitz zeta...
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M(A) is a M-matrix, A is a H-matrix. Invertible H-matrix guarantees convergence of Gauss–Seidel iterative methods. Hurwitz matrix P-matrix Perron–Frobenius...
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Hopf bifurcation (section Routh–Hurwitz criterion)
what is called Hurwitz determinants. Their definition is related to the associated Hurwitz matrix. Proposition 1. If all the Hurwitz determinants c i...
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\\|a_{ij}|&{\text{if }}i=j.\end{cases}}} Hurwitz matrix P-matrix Perron–Frobenius theorem Z-matrix L-matrix M-matrix H-matrix (iterative method) Varga, Richard...
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square matrix or related classes of matrix Hurwitz matrix, a square matrix constructed with coefficients of a real polynomial Parity-check matrix is often...
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Z-matrix, its off-diagonal entries are less than or equal to zero. Hurwitz matrix Metzler matrix David M. Young (2003). Iterative Solution of Large Linear Systems...
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In mathematics, Hurwitz's theorem is a theorem of Adolf Hurwitz (1859–1919), published posthumously in 1923, solving the Hurwitz problem for finite-dimensional...
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Vector fields on spheres (redirect from Radon-Hurwitz number)
non-zero matrix is a similarity transformation, i.e. a product of an orthogonal matrix and a scalar matrix. In quadratic forms, the Hurwitz problem asks...
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bounded away from the positive real axis. Hurwitz matrix Linear complementarity problem M-matrix Q-matrix Z-matrix Perron–Frobenius theorem Kellogg, R. B...
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In mathematics, the Hurwitz zeta function is one of the many zeta functions. It is formally defined for complex variables s with Re(s) > 1 and a ≠ 0,...
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Perron–Frobenius theorem (redirect from Primitive matrix)
minor is positive Hurwitz matrix – Algebraic matrix element to analyze a polynomial by its coefficients Metzler matrix (Quasipositive matrix) Positive operator –...
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B, C and an n x n Hurwitz matrix A, if the pair ( A , B ) {\displaystyle (A,B)} is completely controllable, then a symmetric matrix P and a vector Q satisfying...
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Quaternion (redirect from Matrix representation of quaternions)
numbers; the other being the complex numbers. These rings are also Euclidean Hurwitz algebras, of which the quaternions are the largest associative algebra...
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Gershgorin circle theorem (category Matrix theory)
see Perron–Frobenius theorem. Doubly stochastic matrix Hurwitz matrix Joel Lee Brenner Metzler matrix Muirhead's inequality Bendixson's inequality Schur–Horn...
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to zero asymptotically (i.e., when A − L C {\displaystyle A-LC} is a Hurwitz matrix). For a continuous-time linear system x ˙ = A x + B u , {\displaystyle...
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and the following A2) A2) There is a Hurwitz matrix A {\textstyle A} and a symmetric and positive-definite matrix Σ {\textstyle \Sigma } such that { U...
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relation (zero matrix) as the zero, and the identity relation (identity matrix) as the unity. Central simple algebra Clifford algebra Hurwitz's theorem (normed...
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matrix A is Schur stable (resp. Hurwitz stable). Kreiss constant can be interpreted as a measure of normality of a matrix. In particular, for normal matrices...
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{\displaystyle \Delta _{i}} is the i-th leading principal minor of the Hurwitz matrix associated with f {\displaystyle f} . Using the same notation as above...
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HP CloudSystem (section CloudSystem Matrix)
Hurwitz, a widely recognized industry analyst described CloudSystem Matrix as a linchpin of HP's cloud strategy. She has described CloudSystem Matrix...
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Jones calculus (redirect from Jones matrix)
polarization of the emerging light is found by taking the product of the Jones matrix of the optical element and the Jones vector of the incident light. Note...
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F4 (mathematics) (section Cartan matrix)
the center of the other). They form a ring called the Hurwitz quaternion ring. The 24 Hurwitz quaternions of norm 1 form the vertices of a 24-cell centered...
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