On some tensor inequalities based on the t-product
Zhengbang Cao, Pengpeng Xie
Abstract
In this work, we investigate the tensor inequalities in the tensor t-product formalism. The inequalities involving tensor power are proved to hold similarly as standard matrix scenarios. We then focus on the tensor norm inequalities. The well-known arithmetic-geometric mean inequality, Hölder inequality, and Minkowski inequality are generalized to tensors. Furthermore, we obtain some t-eigenvalue inequalities.
Topics & Concepts
MathematicsTensor productInequalityTensor (intrinsic definition)Tensor product of Hilbert spacesPure mathematicsMinkowski spaceTensor contractionNorm (philosophy)Hölder's inequalityEigenvalues and eigenvectorsKy Fan inequalityTensor densityKantorovich inequalityRearrangement inequalityAlgebra over a fieldMathematical analysisTensor fieldLog sum inequalityExact solutions in general relativityLinear inequalityGeometryPhysicsQuantum mechanicsPolitical scienceLawTensor decomposition and applicationsMatrix Theory and AlgorithmsSparse and Compressive Sensing Techniques