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We construct the Jacobian matrices of linear and angular velocities symbolically and analyse them.
Then the matrix recursion (Xi _{mathsf {B}}) coincides with the stencil map for the matrices of linear operators in the associated basis (mathsf {B}_infty ).
The only required knowledge of a controlled system is that the Markov matrices of linear systems or the partial derivatives of nonlinear systems with respect to control inputs are bounded.
We inputted pairwise tri-distance matrices of linear genetic distance, Φ PT, and R ST into separate PCoAs in GenAlEx.
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The matrix of linear approximation close to equilibrium is expressed by means of the introduced scalar product.
We show that the known traffic rules for eigenvalues of the monodromy matrix of linear Hamiltonian differential and difference systems can be extended also to discrete symplectic systems.
The design of the feedback controller is achieved through the symbolic computation of fundamental solution matrix of linear time-periodic systems in terms of unknown control gains.
The two-dimensional separations for the first time allowed reasonably estimating the amount of statistically branched structures in a matrix of linear ones.
The signals are processed via a matrix of linear filters in order to produce the inputs to a number of sources used for reproduction.
PM10, SO2, and NO2 did not follow a seasonal pattern and were not correlated with temperature (see Additional file 1: Matrix of linear correlation coefficients, Table S1 for an overview of all variables).
Historically, the first ideas leading to vector spaces can be traced back as far as 17th century's analytic geometry, matrices, systems of linear equations, and Euclidean vectors.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com