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Tensors, or hypermatrices, are multi-arrays with more than two
indices. In the last decade or so, many concepts and results in
matrix theory - some of which are nontrivial - have been extended
to tensors and have a wide range of applications (for example,
spectral hypergraph theory, higher order Markov chains, polynomial
optimization, magnetic resonance imaging, automatic control, and
quantum entanglement problems). The authors provide a comprehensive
discussion of this new theory of tensors. Tensor Analysis is unique
in that it is the first book on the spectral theory of tensors; the
theory of special tensors, including nonnegative tensors, positive
semidefinite tensors, completely positive tensors, and copositive
tensors; and the spectral hypergraph theory via tensors, which is
covered in a chapter.
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