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Not all of the transfer matrices are defined for some countable set of energies.
Often, risk matrices are defined using numerical values for event severity and likelihood levels.
Here we study complex-valued linear autoencoders where the components of the training vectors and adjustable matrices are defined over the complex field with the L2 norm.
These coefficient matrices are defined in Eqs.
where matrices, are defined as (3.46).
The channel basis matrices are defined as (9) and (10).
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Therefore, subsequent basis matrices were defined by weighting probesets to maximize conditioning.
The Karcher mean of SPD matrices is defined as the barycenter of these matrices on the manifold of SPD matrices with its Riemannian geometry.
These results are used to derive (oscillatory) asymptotics of the standard short-range and Dollard type S-matrices for the subclasses of potentials where both kinds of S-matrices are defined.
Novel molecular descriptors based on local spectral moments of the bond matrix are defined.
The minimum (maximum), smallest (largest) eigen-subspaces and characteristics matrix are defined in this paper.
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matrices are designated
models are defined
frame are defined
matrices are introduced
matrices are computed
matrices are obtained
matrices are used
matrices are given
matrices are generated
matrices are constructed
matrices are analyzed
matrices are adopted
matrices are kept
matrices are updated
matrices are shared
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