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The variation diminishing property is a characteristic of certain types of mathematical functions, particularly within the context of integral or transformative operations in functional analysis, signal processing, and approximation theory. A function or operator possesses the variation diminishing property if it does not increase the total variation of a function when applied to it.

The WAIFW matrix, which stands for "Who Acquires Infected From Whom," is a concept used in epidemiology and infectious disease modeling. It is a matrix that represents the rates of contact and transmission between different groups within a population. Essentially, it summarizes the interactions between different demographic or social groups, often categorized by age, sex, or other relevant factors.

The Walsh matrix is a specific type of orthogonal matrix that plays an important role in various areas of mathematics, signal processing, and communications. It is named after the mathematician Joseph Walsh.

A matrix is considered to be weakly diagonally dominant if it satisfies a specific condition related to its diagonal elements and the sums of the absolute values of the other elements in the same row.

Weyl-Brauer matrices are specific types of matrices that arise in the representation theory of the symmetric group and the study of linear representations of quantum groups. They are named after Hermann Weyl and Leonard Brauer, who contributed to the understanding of these algebraic structures. In the context of representation theory, Weyl-Brauer matrices can be associated with projective representations. They often come into play when examining interactions between various representations characterized by certain symmetry properties.

The Wigner D-matrix is a mathematical construct used primarily in quantum mechanics and in the field of representation theory of the rotation group SO(3). It plays a significant role in angular momentum theory, particularly in the description of quantum states associated with rotations. ### Definition The Wigner D-matrix is defined for a specific angular momentum quantum state characterized by two quantum numbers: the total angular momentum \( j \) and the magnetic quantum number \( m \).

The Wilkinson matrix is a specific type of structured matrix used in numerical analysis, particularly in the study of matrix algorithms and eigenvalue problems. It is named after the mathematician and computer scientist James H. Wilkinson. The Wilkinson matrix is notable for its properties, especially its sensitivity to perturbations, which makes it useful for testing numerical algorithms for stability and accuracy.

The Wilson matrix, often referred to in the context of particle physics, specifically in the study of quantum field theories and the analysis of interactions, particularly those involving gauge theories and their symmetries. It is typically associated with the systematic approach to constructing effective field theories and the renormalization group. In essence, the Wilson matrix is used to describe the relationship between different physical observables or parameters in a theoretical framework, particularly when considering different energy scales.

The Woodbury matrix identity is a useful result in linear algebra that provides a way to compute the inverse of a modified matrix.

A Z-matrix in mathematics is a specific type of matrix that is characterized by having non-positive off-diagonal entries and positive diagonal entries.

A zero matrix, also known as a null matrix, is a matrix in which all of its elements are equal to zero. It can come in various sizes, such as 2x2, 3x3, or any other \( m \times n \) dimensions, where \( m \) is the number of rows and \( n \) is the number of columns.