2,391 research outputs found
Spectral radius of Hadamard product versus conventional product for non-negative matrices
We prove an inequality for the spectral radius of products of non-negative
matrices conjectured by X. Zhan. We show that for all non-negative
matrices and , , where represents the Hadamard product.Comment: 4.1 page
The possible shapes of numerical ranges
Which convex subsets of the complex plane are the numerical range W(A of some
matrix A? This paper gives a precise characterization of these sets. In
addition to this we show that for any A there exists a symmetric matrix B of
the same size such that W(A)=W(B).Comment: 4 page
An Explicit Formula for the Matrix Logarithm
We present an explicit polynomial formula for evaluating the principal
logarithm of all matrices lying on the line segment
joining the identity matrix (at ) to any real matrix (at )
having no eigenvalues on the closed negative real axis. This extends to the
matrix logarithm the well known Putzer's method for evaluating the matrix
exponential.Comment: 6 page
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