It is proved that the Kronecker product of two matrices with the Perron-Frobenius property is a matrix with the Perron-Frobenius property. Moreover, we also prove that the Kronecker product of two GM-matrices is a GM-matrix when one has real eigenvalues, the same is true for inverse GM-...
We close this section by noting that Section 3.3.2 provides an example of a deterministic basis with small block-coherence, which is obtained by modifying the Kronecker product of the canonical and Fourier bases. (This basis is then used to prove the RIP for partial random circulant matrices....
Second, we turn to parabolic systems ≔∂tu−div(A∇u)+b⋅∇u+cu=0,inQT≔(0,T)×Ωwhere the question of coupling of the coefficients is even more restraining, A=I⊗a,i.e.Aijαβ(x)=δαβaij(x)where I∈RN×N the identity matrix and thus δαβ the Kronecker del...
we combine the Kronecker product, Hadamard product with numerical rang of matrices, discuss the relations between the Kronecker product, Hadamard product with numerical rang of matrices, and illustrate that the kippenhahn curve consists of consists of one ellipse whose foci are and axis has a ...
In this paper, let A and C be deoted 4脳4 reducible companion matrices, we study the property of the Kippenhahn curve C_R (C) and of the numerical rang W(A) being an elliptic disc by making use of matrices Kronecker sum, Kronecker product and Hadamard product and the Kippenhahn ...
These conditions are based on solving the Lyapunov equation for 2-D continuous systems using the Kronecker product and lead to a simple test for the VSHP property. It requires testing the eigenvalues of three constant matrices only and is simpler than existing polynomial tests....
Kronecker productunitary matrixThe present paper is concerned with the study of the density property in Fr茅chet-domains of Op * -algebras, abbreviated F-domains. The density property was introduced by S. Heinrich for locally convex spaces and was studied by K. D. Bierstedt and J. Bonet for...
Kronecker productlinear modelnonlinear interactionPrimary 62G05secondary 62G0862G20We consider local polynomial estimation for varying coefficient models and derive corresponding equivalent kernels that provide insights into the role of smoothing on the data and fill a gap in the literature. We show ...
Property (-SR)Kronecker productCorona graphBulletin of the Malaysian Mathematical Sciences Society - Let G be a simple graph and A(G) be its adjacency matrix. We say that the graph G satisfies reciprocal eigenvalue property (or simply,......
Then the matrix NNT can be written as follows: NNT=[B11⋯B1m⋮⋱⋮Bm1⋯Bmm], where Bij=[(k−λ1)In+(λ1−λ2)Jn]δij+λ2Jn, and δij is the Kronecker delta. Theorem 3.1 Let D(v,k,λ1,λ2,m,n) be a SGDD with the dual property, and let N be the incidence...