Charles R. Johnson

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20022026

most citedTotal positivity of sums, Hadamard products and Hadamard powers: Results and counterexamples

37 citations · 96 across the 28 of their papers we have counts for

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math.OA2005

Eigenvalues of Words in Two Positive Definite Letters

Christopher J Hillar, Charles R Johnson

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…

math.OA2005

Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices

Christopher Hillar, Charles R. Johnson

We define a word in two positive definite (complex Hermitian) matrices $A$ and $B$ as a finite product of real powers of $A$ and $B$ . The question of which words have only positive…

math.OA2005

Positive eigenvalues and two-letter generalized words

Christopher Hillar, Charles R. Johnson, Ilya M. Spitkovsky

A generalized word in two letters $A$ and $B$ is an expression of the form $W = A^{α_{1}} B^{β_{1}} A^{α_{2}} B^{β_{2}} ... A^{α_{N}} B^{β_{N}}$ in which the exponents $α_{i}$ , $β_{i}$ are nonzero real n…

math.OA2005

Absolutely Flat Idempotents

Jonathan M. Groves, Yonatan Harel, Christopher J. Hillar +2

A real $n$ -by- $n$ idempotent matrix $A$ with all entries having the same absolute value is called {\it absolutely flat}. We consider the possible ranks of such matrices and herein…