∥ ⋅ ∥ refers to the Euclidean vector norm; the notation A ⊗ B stands for the Kronecker product of matrices A and B. If A is a matrix, λ min denotes the minimum eigenvalue.
To shorten our notation the norm (Vert cdot Vert ) will denote (Vert cdot Vert _{L_{2}(0,1)}).
For Banach spaces and, we denote by the Banach space of all bounded linear operators from to equipped with the operator norm, and use the notation in place of.
There is widespread use of the language and results of linear algebra, real analysis, and functional analysis (with its simplifying notation of norms, vector spaces, and operators).
Using the earlier notation, p-norm defines the output of the lth group as o_{l}=left(sumlimits_{k=0}^{K-1}|z_{lK+k}|^{p}right)^{1/p}.
We shall use the following notation for the norms: (|x|) is an X-norm, (|y|_{ast}) is an (mathbf{X}^{ast} -norm, and (|x|_{mathbf{X}^{ast} -normorm.
These musicians researched university archives, the Library of Congress and the private precincts of individual collectors to find long out-of-print arrangements fortuitously set down before the era of recorded sound, when improvisation, not musical notation, was the norm.
The notation denotes the norm of bounded linear operators for all, where.
This primarily allows them to avoid the summation of squared F-norms and traces in the notation for their algorithm.
For simplicity of notation, hereafter we denote by the Lebesgue space norm, denotes norm, and write equivalent norm instead of norm.
