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Showing 1 to 8 of 8 for “"2)-matrices"”.
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Two problems in iterative nonlinear maps
… of a logistic map defined in real 2 x 2 matrices. We show how these boundaries are of a mixed type, combining fractal and smooth regions. We find in these boundaries a very complex distribution of transient scaling behaviors that can mask in some regions the fractal nature of the set. We …
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An Examination of the Yang-Baxter Equation
… from the viewpoint of the algebraic product of matrices, i.e., the composition of linear maps, with the intent of characterizing the solutions of the Yang-Baxter equation.</p> <p>We begin by examining the simple case of 2<strong></strong>2 matrices where it is possible to fully characterize the …
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Exploring the Numerical Range of Block Toeplitz Operators
… of the numerical range for any \(2 \times 2\) matrices \(A_0\) and \(A_1\). We finish by providing examples of flat portions on the boundary of the numerical range when \(A_0, A_1 \in M_n(\mathbb{C})\), for \(3 \leq n \leq 5\).</p>
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The proxy point method for rank-structured matrices
… to reduce computation and storage cost for dense matrices defined by interactions between many bodies. The main bottleneck for their application is the expensive computation required to represent a matrix in a rank-structured matrix format which involves compressing specific matrix blocks into …
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ON THE LYAPUNOV-TYPE DIAGONAL STABILITY
… to common diagonal Lyapunov solutions on two matrices of order one less. An enhanced statement of this result based on the Schur complement formulation is presented here along with a shorter and purely matrix-theoretic proof. We develop a number of extensions to this result, and formulate the …
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Asymptotic formulae for certain arithmetic functions produced by fractional linear transformations
… arising from certain $2 \times 2$ matrices, establish asymptotic formulae for averages of these functions, and explore certain maps that arise from considering the leading terms of these averages. We further generalize to a larger class of maps by introducing real moments, which …
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Banded matrices with banded inverses
… we tend to focus on the ranks of the block matrices that are present in the banded matrix. We consider mainly the two factor 2-by- 2 block matrix and the three factor 2-by-2 block matrix cases. We prove that the ranks of the blocks in the larger banded matrix need to necessarily conform to a …