A necessary and sufficient condition for the positivedefiniteness of interval symmetric matrices - Shi, Gao - 1986 () Citation Context ...to obtain more sufficient conditions. When the vertices of the matrix family are symmetric, the corresponding uncertain dynamical systems are stable if and only ...
Therefore, the Hessian is always a symmetric matrix. The Hessian matrix plays a prominent role in exploring the sufficiency conditions for optimality. Note that a square matrix is positive-definite if (a) the determinant of the Hessian matrix is positive (i.e., |H| > 0) or (b) all its...
Condition such that the symmetric matrix has only positive eigenvalues My attempt: $$ \begin{vmatrix} 1-\lambda & b\\ b & a-\lambda \end{vmatrix} =0$$ $$(1-\lambda)(a-\lambda)-b^2=0$$ $$a-\lambda-a\lambda+\lambda^2-b^2=0$$ $$\lambda^2+(-1-a)\lambda +a-b^2=0$...
Consider a symmetric matrix A. (a) Prove that a necessary condition for A to be positive definite is that all entries on the diagonal are strictly positive. (b) Prove that a necessary condition for A to be negative semidefinite is that all entries on ...
To define the boundary value problem under study, we assume a second order elliptic operator whose coefficients aij form a 2 × 2 symmetric matrix A. We suppose that aij∈ L∞(B) and that ∑i,j=12aij(x)ξiξj≥cA(ξ12+ξ22), for each ξ = (ξ1, ξ2)∈ ℝ2 and a.a. x...
Intensity MatrixCharacteristic EquationsState ProbabilitiesTechnical system consisting of two independent subsystems (e.g. hybrid car) is considered. Graduated state graph being homogenous ergodic system of symmetric structure is constructed for the system. Differential Kolmogorov equations, describing homogenous...
We also use optional cookies for advertising, personalisation of content, usage analysis, and social media. By accepting optional cookies, you consent to the processing of your personal data - including transfers to third parties. Some third parties are outside of the European Economic Area, with...
the GSM of the element is combined into the global one of the structure, this structural stiffness matrix becomes symmetric and satisfies both the rigid body rule and incremental force and moment equilibrium (IFE) conditions, which are basically two fundamental conditions for analysis of mechanics. ...
We remark that the restriction \( \,\mu +\mu _c \ge 0 \, \) is in accordance with the Legendre-Hadamard condition for three-dimensional isotropic Cosserat materials (without fiber reinforcement) established in [9]. 5.2 Example: Conventional elastic matrix material with fiber reinforcement Consi...
where κ=[κij] is a symmetric matrix of heat conductivities. We seek the three conductivities c1=κ11, c2=κ22 and c3=κ12=κ21. Thus, the inverse problem has 3 degrees of freedom (DOFs) at each node. We expand the three unknown functions in the shape functions, i.e., (122)ci...