It is shown that a matrix with non-negative entries has non-negative determinant if in each row the elements decrease, by steadily smaller amounts, as one proceeds (in either direction) away from the main diagonal. This condition suffices to establish non- negativity of the determinant for ...
The well-known absolute bound condition for a primitive symmetric association scheme ( X , S ) gives an upper bound for | X | in terms of | S | and the minimal non-principal multiplicity of the scheme. In this paper we prove another upper bounds for | X | for an arbitrary primitive...
We point out that all thePT-symmetric... A Mostafazadeh - 《Journal of Mathematical Physics》 被引量: 1066发表: 2002年 On the Digraph of a Unitary Matrix We give a necessary condition, called strong quadrangularity, for a digraph to be the digraph of a unitary matrix. With the use of...
Utilizing NASIR Galerkin Finite Volume Analyzer for 2D Plane Strain Problems under Static and Vibrating Concentrated Loads A Numerical Analyzer for Scientific and Industrial Requirements (NASIR) software which utilizes novel matrix free Finite Volume is applied for solving plane strain solid state problems...
Let be a real symmetric block-matrix with A and B positive definte. Then M is positive definte if and only if. An application for this result to the stability of constant coefficient linear system is presented.关键词: Positive definite condition block-matrix linear ordinary differential equatio...
ConditionEigenvaluesMatrixPositiveSymmetricSymmetric matrix Replies: 8 Forum:Calculus and Beyond Homework Help POTWA 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 trace of ##L...
We study the smallest singular value of a square random matrix with i.i.d. columns drawn from an isotropic log-concave distribution. An important example is obtained by sampling vectors uniformly dis- tributed in an isotropic convex body. We deduce that the condition number of such matrices is...
The boundary condition prescribed on the over-prescribed boundary can be introduced in the boundary element matrix equation, which can be solved for the unknown boundary values on the incompletely-prescribed boundary. Due to the ill-posedness of the problem, the matrix involved is severely ill-...
n <= m, the condition Riemannian structure as follows: For a given matrix A the tangent space at A is equipped with the Hermitian inner product obtained by multiplying the usual Frobenius inner product by the inverse of the square of the smallest singular value of A denoted sigma(n)(A)....
The above set of equations can also be written in matrix form as (11)[δ−qκκδ+q][AfAb]=0 and by setting the determinant equal to zero, we obtain (12)δ=±q2+k2 Equation (12) is the dispersion relation for the periodic structure in the SMF. Figure 17.5 represents dispersion cu...