Displaying similar documents to “The three point pick problem on the bidisk.”

Zero-term rank preservers of integer matrices

Seok-Zun Song, Young-Bae Jun (2006)

Discussiones Mathematicae - General Algebra and Applications

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The zero-term rank of a matrix is the minimum number of lines (row or columns) needed to cover all the zero entries of the given matrix. We characterize the linear operators that preserve the zero-term rank of the m × n integer matrices. That is, a linear operator T preserves the zero-term rank if and only if it has the form T(A)=P(A ∘ B)Q, where P, Q are permutation matrices and A ∘ B is the Schur product with B whose entries are all nonzero integers.

A complete characterization of invariant jointly rank- convex quadratic forms and applications to composite materials

Vincenzo Nesi, Enrico Rogora (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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The theory of compensated compactness of Murat and Tartar links the algebraic condition of rank- convexity with the analytic condition of weak lower semicontinuity. The former is an algebraic condition and therefore it is, in principle, very easy to use. However, in applications of this theory, the need for an efficient classification of rank- convex forms arises. In the present paper, we define the concept of extremal -forms  and characterize them in the rotationally invariant...