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Table 1 Notations

From: Deep data analysis via physically constrained linear unmixing: universal framework, domain examples, and a community-wide platform

Notation Remarks
\(A \in {\mathcal{R}}^{m \times n}\) Capital case letter generally denotes a matrix of size m × n
\(a \in {\mathcal{R}}^{m}\) Lower case letter denotes a column vector of length m
A ij or a i A scalar/element from the matrix at location (i,j) or a vector element at i
||A|| F \(\sqrt {\mathop \sum \nolimits_{i = 1}^{m} \mathop \sum \nolimits_{j = 1}^{n} A_{ij}^{2} }\)—square root of the sum of the squares of all the elements of the matrix
||A||1 \(\sum\nolimits_{i = 1}^{m} {\sum\nolimits_{j = 1}^{n} {\left| {A_{ij} } \right|} }\)—sum of absolute values of all the elements. Here absolute value means the non-negative value without its sign
||a||2 \(\sqrt {\sum\nolimits_{i = 1}^{m} {a_{i}^{2} } }\)—square root of the sum of the squares of all the elements of the vector
μ Mean of a vector
KL(P||Q) Defines the similarity between two matrices P and \(Q\) as \(\sum\nolimits_{i = 1}^{m} {\sum\nolimits_{j = 1}^{n} {\left( {P_{ij} \log \frac{{P_{ij} }}{{Q_{ij} }} } \right)} }\)