Tensor Transpose and Its Properties

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Pan, Ran;
  • Subject: Computer Science - Numerical Analysis | Mathematics - Numerical Analysis
    arxiv: Quantitative Biology::Genomics

Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor transpose are stud... View more
  • References (20)
    20 references, page 1 of 2

    [1] B. W. Bader and T. G. Kolda, Algorithm 862: MATLAB tensor classes for fast algorithm prototyping, ACM Trans. Math. Software, 32 (2006), pp. 635{653.

    [2] B. W. Bader and T. G. Kolda, MATLAB Tensor Toolbox, Version 2.2., Available at http://csmr.ca.sandia.gov/ tgkolda/TensorToolbox/, (2007).

    [3] J. D. Carroll and J. J. Chang, Analysis of individual di erences in multidimensional scaling via an N-way generalization of Eckart-Young decomposition, Psychometrika, 35 (1970), pp. 283{319.

    [4] R. B. Cattell, Parallel proportional pro les and other principles for determining the choice of factors by rotation, Psychometrika, 9 (1944), pp. 267{283.

    [5] R. B. Cattell, The three basic factor-analytic research designstheir interrelations and derivatives, Psych. Bull., 49 (1952), pp. 452{499.

    [6] Z. Chen, L. Lu, Z. Liu The eigenvalue problems for tensor and tensor transposition (Chinese), Journal of Xiamen University (Natural Science), Vol. 51, No. 3, (2012) [9] S. C. Deerwester, S. T. Dumais, T. K. Landauer, G. W. Furnas, and R. A. Harshman, Indexing by latent semantic analysis, J. Amer. Soc. Inform. Sci., 41 (1990), pp. 391{407.

    [11] M. Hassani, Derangements and Applications, J. Integer Seq. 6, No. 03.1.2, (2003), pp. 1{8.

    [12] F. L. Hitchcock, Multilple invariants and generalized rank of a p-way matrix or tensor, J. Math. Phys., 7 (1927), pp. 39{79.

    [13] F. L. Hitchcock, The expression of a tensor or a polyadic as a sum of products, J. Math.Phys., 6 (1927), pp. 164{189.

    [14] N. Jacobson, Basic Algebra(I) (2nd Edition), New York: W.H. Freeman and Company, (1985).

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