Theoretical or Mathematical/ matrix algebra/ necessary and sufficient conditionpositive-definitenessinterval symmetric matrices/ C1110 AlgebraA necessary and sufficient condition for the positive-definiteness of interval symmetric matrices is obtained, and a useful application is shown....
Condition Eigenvalues Matrix Positive Symmetric Symmetric matrix Replies: 8 Forum: Calculus and Beyond Homework Help POTW A Linear Operator with Trace Condition Let ##V## be a finite dimensional vector space over a field ##F##. If ##L## is a linear operator on ##V## such that the ...
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 ...
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...
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...
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...
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. ...
Periodicity and Application for a kind of n-dimensional Arnold-type Transformation The necessary and sufficient condition about the existence of periodicity for the general Arnold matrix transformation had been given in literatures. The ... JZ Wang,YL Wang,MQ Wang - IEEE 被引量: 4发表: 2007年 ...
9.Nine equivalent conditions of real idempotent matrix are given and proved, and one equivalent condition of real symmetric idempotent matrix is also given in this paper.给出并证明了实幂等矩阵的九个等价条件,以及实对称幂等矩阵的一个等价条件。 10.Equivalent Conditions over a Non-negative Commutative...
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...