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When a Hermitian linear operator A is slightly perturbed, by how much can its invariant subspaces change? Given some approximations to a cluster of neighboring eigenvalues and to the corresponding eigenvectors of a real symmetric matrix, and given a lower bound S > 0 for the gap that separates the cluster from all other eigenvalues, how much can the… (More)
For any n-by-n complex matrix A, we use the joint numerical range W (A, A 2 ,. .. , A k) to study the polynomial numerical hull of order k of A, denoted by V k (A). We give an analytic description of V 2 (A) when A is normal. The result is then used to characterize those normal matrices A satisfying V 2 (A) = σ(A), and to show that a unitary matrix A… (More)
Given a symmetric n X n matrix A and n numbers rl," " r n , necessary and sufficient conditions for the existence of a matrix B, with a given zero pattern, with is relaxed, then such a matrix B exists if and only if the sum r 1 + ... +rn is equal to half the sum of the elements of A. The case where A and B are nonnegative matrices is solved as well.
This volume, misleadingly subtitled 'Creative Writing in Mathematics and Sci-ence', is an anthology of poems, essays, plays, short stories and biographies, each of which has a mathematical or scientific theme. It arose from a series of workshops at the Banff Centre for the Arts and the Banff International Research Station for Mathematical Innovation and… (More)