Charles R. Johnson

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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…