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- Christopher J. Hillar, Lek-Heng Lim
- J. ACM
- 2013

We prove that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard. Our list includes: determining the feasibility of a system of bilinearâ€¦ (More)

Let A be a commutative Noetherian ring, and let R = A[X] be the polynomial ring in an infinite collection X of indeterminates over A. Let SX be the group of permutations of X. The group SX acts on Râ€¦ (More)

- Charles R. Johnson, Christopher J. Hillar
- SIAM J. Matrix Analysis Applications
- 2002

The question of whether all words in two real positive definite letters have only positive eigenvalues is addressed and settled (negatively). This question was raised some time ago in connection withâ€¦ (More)

- Christopher J. Hillar, Darren L. Rhea
- The American Mathematical Monthly
- 2007

Much less known, however, is that there is a description of Aut(G), the automorphism group of G. The first compete characterization that we are aware of is contained in a paper by Ranum [1] near theâ€¦ (More)

- Christopher J. Hillar, Troels Windfeldt
- J. Comb. Theory, Ser. B
- 2008

The study of graph vertex colorability from an algebraic perspective has introduced novel techniques and algorithms into the field. For instance, it is known that k-colorability of a graph G isâ€¦ (More)

- Christopher J. Hillar, Friedrich T. Sommer
- IEEE Transactions on Information Theory
- 2015

Sparse coding or sparse dictionary learning has been widely used to recover underlying structure in many kinds of natural data. Here, we provide conditions guaranteeing when this recovery isâ€¦ (More)

A long-standing conjecture asserts that the polynomial p(t) = Tr[(A + tB)m] has positive coefficients when m is a positive integer and A and B are any two n Ã— n positive definite Hermitian matrices.â€¦ (More)

Let K be a totally real number field with Galois closure L. We prove that if f âˆˆ Q[x1, . . . , xn] is a sum of m squares in K[x1, . . . , xn], then f is a sum of 4m Â· 2 ([L : Q] + 1 2 ) squares inâ€¦ (More)

A new algorithm is proposed for a) unsupervised learning of sparse representations from subsampled measurements and b) estimating the parameters required for linearly reconstructing signals from theâ€¦ (More)

- Christopher J. Hillar, Ram Mehta, Kilian Koepsell
- 2014 IEEE International Conference on Imageâ€¦
- 2014

The Hopfield network is a well-known model of memory and collective processing in networks of abstract neurons, but it has been dismissed for use in signal processing because of its small patternâ€¦ (More)