Algebraic connectivity of an even uniform hypergraph
Journal of Combinatorial Optimization
On determinants and eigenvalue theory of tensors
Journal of Symbolic Computation
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The subject of this thesis is best described as the study of a few new problems in multilinear algebra that are analogous to important classical problems in numerical linear algebra. Among other things, we will study the problem of finding a best low rank approximation to a tensor, a symmetric tensor, and a nonnegative tensor; define a notion of eigenvalues and eigenvectors for symmetric tensors and a notion of singular values and singular vectors for general tensors; we apply our multilinear spectral theory to hypergraphs in a way that parallels spectral graph theory, and to nonnegative tensors in a way that parallels the results of Perron-Robenius; we will also study an extension of nonnegative matrix factorization to nonnegative tensors.