In mathematics, a Hurwitz matrix, or Routh–Hurwitz matrix, in engineering stability matrix, is a structured real square matrix constructed with coefficients...

mathematician Adolf Hurwitz independently proposed in 1895 to arrange the coefficients of the polynomial into a square matrix, called the Hurwitz matrix, and showed...

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...

non-singular symmetric M-matrix is sometimes called a Stieltjes matrix. Hurwitz matrix P-matrix Perron–Frobenius theorem Z-matrix H-matrix Fujimoto, Takao &...

theory, these are referred to as stoquastic operators. Hurwitz matrix M-matrix Metzler matrix P-matrix Bravyi, Sergey; DiVincenzo, David P.; Oliveira, Roberto...

matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...

differential equation M-matrix P-matrix Q-matrix, a specific kind of Metzler matrix Z-matrix Hurwitz matrix Stochastic matrix Positive systems Berman...

Hurwitz matrix Hurwitz numbers Hurwitz polynomial Hurwitz problem Hurwitz quaternion order Hurwitz quaternion Hurwitz scheme Hurwitz surface Hurwitz zeta...

, 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...

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...

what is called Hurwitz determinants. Their definition is related to the associated Hurwitz matrix. Proposition 1. If all the Hurwitz determinants c i...

\\|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...

square matrix or related classes of matrix Hurwitz matrix, a square matrix constructed with coefficients of a real polynomial Parity-check matrix is often...

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...

In mathematics, Hurwitz's theorem is a theorem of Adolf Hurwitz (1859–1919), published posthumously in 1923, solving the Hurwitz problem for finite-dimensional...

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...

bounded away from the positive real axis. Hurwitz matrix Linear complementarity problem M-matrix Q-matrix Z-matrix Perron–Frobenius theorem Kellogg, R. B...

numbers; the other being the complex numbers. These rings are also Euclidean Hurwitz algebras, of which the quaternions are the largest associative algebra...

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...

minor is positive Hurwitz matrix – Algebraic matrix element to analyze a polynomial by its coefficients Metzler matrix (Quasipositive matrix) Positive operator –...

see Perron–Frobenius theorem. Doubly stochastic matrix Hurwitz matrix Joel Lee Brenner Metzler matrix Muirhead's inequality Bendixson's inequality Schur–Horn...

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,...

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...

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...

relation (zero matrix) as the zero, and the identity relation (identity matrix) as the unity. Central simple algebra Clifford algebra Hurwitz's theorem (normed...

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...

{\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...

Hurwitz, a widely recognized industry analyst described CloudSystem Matrix as a linchpin of HP's cloud strategy. She has described CloudSystem 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...

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...