Natural projectors in tensor spaces.
New bounds for the minimum eigenvalue of 𝓜-tensors
A new lower bound and a new upper bound for the minimum eigenvalue of an 𝓜-tensor are obtained. It is proved that the new lower and upper bounds improve the corresponding bounds provided by He and Huang (J. Inequal. Appl., 2014, 2014, 114) and Zhao and Sang (J. Inequal. Appl., 2016, 2016, 268). Finally, two numerical examples are given to verify the theoretical results.
New criteria for H-tensors and an application
Some new criteria for identifying H-tensors are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor are given. Advantages of results obtained are illustrated by numerical examples.
New iterative codes for𝓗-tensors and an application
New iterative codes for identifying 𝓗 -tensor are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor, i.e., an even-degree homogeneous polynomial form are given. Advantages of results obtained are illustrated by numerical examples.
Norm estimates for functions of two commuting matrices.
Norm estimates for solutions of matrix equations AX-XB=C and X-AXB=C
Let A, B and C be matrices. We consider the matrix equations Y-AYB=C and AX-XB=C. Sharp norm estimates for solutions of these equations are derived. By these estimates a bound for the distance between invariant subspaces of matrices is obtained.
On a result of Williamson.
On matrix groups defined by certain polynomial identities
On Nambu bracket representations of 3-algebras.
On Projections in the Symmetric Power Space.
On reducing and deflating subspaces of matrices.
On SAP Fields.
On the bounds for the spectral and norms of the Khatri-Rao product of Cauchy-Hankel matrices.
On the connection between Kronecker and Hadamard convolution products of matrices and some applications.
On the trace characterization of the joint spectral radius.
On two matrix derivatives by Kollo and von Rosen.
The article establishes relationships between the matrix derivatives of F with respect to X as introduced by von Rosen (1988), Kollo and von Rosen (2000) and the Magnus-Neudecker (1999) matrix derivative. The usual transformations apply and the Moore-Penrose inverse of the duplication matrix is used. Both X and F have the same dimension.
Paare alternierender Formen.
Produit tensoriel topologique de corps valués
Projections of tensor spaces
Rank of tensors of -out-of- functions: An application in probabilistic inference
Bayesian networks are a popular model for reasoning under uncertainty. We study the problem of efficient probabilistic inference with these models when some of the conditional probability tables represent deterministic or noisy -out-of- functions. These tables appear naturally in real-world applications when we observe a state of a variable that depends on its parents via an addition or noisy addition relation. We provide a lower bound of the rank and an upper bound for the symmetric border rank...