EAN: 9784431554585

SPRINGERBRIEFS IN STATISTICS ALGEBRAIC AND CO...

This book provides comprehensive summaries of theoretical (algebraic) and computational aspects
of tensor ranks  maximal ranks  and typical ranks  over the real number field. Although tensor
ranks have been often argued in the complex number field  it should be emphasized that this
book treats real tensor ranks  which have direct applications in statistics. The book provides
several interesting ideas  including determinant polynomials  determinantal ideals  absolutely
nonsingular tensors  absolutely full column rank tensors  and their connection to bilinear maps
and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in
details  global theories such as the Jacobian method are also reviewed in details. The book
includes as well an accessible and comprehensive introduction of mathematical backgrounds  with
basics of positive polynomials and calculations by using the Groebner basis. Furthermore  this
book provides insights into numerical methods of finding tensor ranks through simultaneous
singular value decompositions.

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