GJMS-like operators on symmetric 2-tensors and their gravitational duals

On the X-ray Transform of Planar Symmetric 2-tensors

In this paper we study the attenuated X-ray transform of 2-tensors supported in strictly convex bounded subsets in the Euclidean plane. We characterize its range and reconstruct all possible 2-tensors yielding identical X-ray data. The characterization is in terms of a Hilbert-transform associated with A-analytic maps in the sense of Bukhgeim.

Symmetric 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

The Projective Quarter Symmetric Metric Connections and Their Curvature Tensors

Symmetric Tensors and Symmetric Tensor Rank

A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric sum of outer product of vectors. A rank-1 order-k tensor is the outer product of k non-zero vectors. Any symmetric tensor can be decomposed into a linear combination of rank-1 tensors, each of them being symmet...

Block 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...