flash.geom.Matrix Public Properties Show Inherited Public Properties PropertyDefined By determinant : Number [read-only] A Number that determines whether a matrix is invertible. Matrix3D position : Vector3D A Vector3D object that holds the position, the 3D coordinate (x,y,z) of a display ...
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Use these short and self-contained lecture notes on matrix algebra for self-study or to complement your course material.
First, since the deformation gradient tensor has nine independent components, an atom in a three-dimensional system must have, at a minimum, three neighbors. Second, in order for ηα to be invertible, it must be the case that these neighbors span three-dimensional space, i.e. the atom ...
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A necessary and sufficient condition is given for $${\left(\begin{smallmatrix}A &\enspace C\\ X &\enspace B \end{smallmatrix}ight)}$$ to be a right (left) invertible operator for some $${X \in \mathcal {B}(\mathcal {H}_{1},\, \mathcal {H}_{2})}$$ . Furthermore, ...
Next, we addressed theregressionproblem, i.e., predicting the steady-state abundance of the exogenous species. For the GLV model (with the interaction matrixAbeing invertible, which is almost surely true for randomly constructed matrices), our analytical derivations discovered a surprisingly simple li...
5. All proofs are deferred to the Appendix. For every vector vv=(v1,…,vp)T, denote |vv|2=∑l=1pvl2, |vv|1=∑l=1p|vl|, and |vv|∞=max1≤l≤p|vl|. Moreover, we use supp(vv)={1≤l≤p∣vl≠0} as the support of the vector vv. For every matrix AA∈Rp1×p2, ...
If the matrix A is invertible, there always exist periodic communication sequences (which can be constructed using the algorithm given in this paper) such that Lei Zhang received his Ph.D. in Mechanical Engineering in 2005 from the University of Maryland College Park, College Park, Maryland USA...