Einstein productMultilinear time invariant control systemsThis paper devotes to the generalized eigenvalues for even order tensors. We extend classical spectral theory for matrix pairs to the multilinear case, including the generalized Schur decomposition, the Ger?gorin circle theorem, and the Bauer-Fike...
, then $$\begin{aligned}f(x):=f_1(z)+jf_2(z).\end{aligned}$$ the tensor product \({\mathbb {h}}\otimes \mathbb {c}\) can be equipped with the complex structure induced by the second factor. the slice function f is then called slice-regular if f is holomorphic. if a ...
The discrete operator has a tensor product 30 Nprocs MFLOPS 2 172.50 4 322.03 8 586.29 16 1006.60 32 1412.73 Table 6: Parallel ARPACK on T3D Shared Memory structure from the discrete Laplacian plus a diagonal matrix from the potential. The resulting matrix has a block structure consisting of ...
Spectral Method with the Tensor-Product Nodal Basis for the Steklov Eigenvalue Problem[J] . Xuqing Zhang,Yidu Yang,Hai Bi,Daoyi Dong.Mathematical Problems in Engineering . 2013Zhang X Q, Yang Y D, Bi H. Spectral method with the tensor-product nodal basis for the Steklov eigenvalue problems...
We investigate properties of the determinants of tensors, and their applications in the eigenvalue theory of tensors. We show that the determinant inherits many properties of the determinant of a matrix. These properties include: solvability of polynomial systems, product formula for the determinant ...
By considering a higher order singular value decomposition of a tensor, we show that higher order singular values are the square root of the eigenvalues of the product of the tensor and its conjugate transpose. This result is similar to that in matrix case. Also we study an eigenvalue ...
In this paper, some bounds on the minimum H-eigenvalue of a Z-tensor and the Fan product of Z-tensors are given. By applying the bounds, we obtain some criteria for M-tensors and the positive definiteness of the Fan product of Z-tensors, and give some properties for the determinant ...
L. Besse that the warped product conclusion holds without any restriction on the trace.MERTONDEPARTMENT OF MATHEMATICSGABEDEPARTMENT OF MATHEMATICSProceedings of the American Mathematical SocietyG. Merton, Codazzi tensors with two eigenvalue functions, Proc. Amer. Math. Soc. 141 (2013), no. 9, ...
Some inequalities on the minimum H-eigenvalue of the Fan product of Z-tensors - ScienceDirectJihong Shen a bYue Wang aChangjiang Bu a bLinear Algebra and its Applications
geG M geG M 0.2) where dV~ is the volume element (possibly degenerate) associated to the tensor (/~*g* ds 2. The n-conj'ormal volume of M is then defined to be V,,(n,M ) = inf V,.(n,c/)) (1.3) where q~ runs over all non-degenerate conformal mappings of M into S"....