Positive definiteness of paired symmetric tensors and elasticity tensors
نویسندگان
چکیده
منابع مشابه
Positive Semi-definiteness of Generalized Anti-circulant Tensors
Anti-circulant tensors have applications in exponential data fitting. They are special Hankel tensors. In this paper, we extend the definition of anti-circulant tensors to generalized anticirculant tensors by introducing a circulant index r such that the entries of the generating vector of a Hankel tensor are circulant with module r. In the special case when r=n, where n is the dimension of the...
متن کاملSymmetric nonnegative tensors and copositive tensors
Article history: Received 6 December 2012 Accepted 11 March 2013 Available online 8 April 2013 Submitted by R.A. Brualdi AMS classification: 15A18 15A69
متن کاملDivergence-free positive symmetric tensors and fluid dynamics
We consider d× d tensors A(x) that are symmetric, positive semi-definite, and whose rowdivergence vanishes identically. We establish sharp inequalities for the integral of (detA) 1 d−1 . We apply them to models of compressible inviscid fluids: Euler equations, Euler–Fourier, relativistic Euler, Boltzman, BGK, etc... We deduce an a priori estimate for a new quantity, namely the space-time integr...
متن کاملBlock tensors and symmetric embeddings
Well known connections exist between the singular value decomposition of a matrix A and the Schur decomposition of its symmetric embedding sym(A) = ([ 0A ; A 0 ]). In particular, if σ is a singular value of A then +σ and −σ are eigenvalues of the symmetric embedding. The top and bottom halves of sym(A)’s eigenvectors are singular vectors for A. Power methods applied to A can be related to power...
متن کامل4th Order Symmetric Tensors and Positive ADC Modelling
High Order Cartesian Tensors (HOTs) were introduced in Generalized DTI (GDTI) to overcome the limitations of DTI. HOTs can model the apparent diffusion coefficient (ADC) with greater accuracy than DTI in regions with fiber heterogeneity. Although GDTI HOTs were designed to model positive diffusion, the straightforward least square (LS) estimation of HOTs doesn’t guarantee positivity. In this ch...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2018
ISSN: 0377-0427
DOI: 10.1016/j.cam.2018.01.025