A Complex Hadamard matrix is a special type of square matrix that is characterized by its entries being complex numbers, specifically, the matrix's entries must satisfy certain orthogonality properties.
In mathematics, a compound matrix is a type of matrix that is derived from another matrix, specifically an \( n \times n \) matrix, to represent all possible combinations of its elements. The term is often used in the context of determinants. A compound matrix typically yields a matrix whose entries consist of the determinants of all possible \( k \times k \) submatrices of the original \( n \times n \) matrix.
Pierre Fayet is a prominent French physicist known for his contributions to the fields of particle physics and quantum field theory. He has been involved in significant research related to the standard model of particle physics, including work on the Higgs boson and other fundamental aspects of the theory.
Pierre-Louis Maupertuis (1698–1759) was a French mathematician, astronomer, biologist, and philosopher. He is best known for his work in the fields of mathematics and physics, particularly in relation to the principles of mechanics and the study of the shape of the Earth.
Pierre Weiss (1865–1940) was a French physicist known for his contributions to the fields of magnetism and crystallography. He is particularly noted for his work on magnetic properties of materials and the Weiss theory of ferromagnetism. Weiss introduced the concept of the "Weiss domain," which describes the formation of small regions within ferromagnetic materials where the magnetic moments of atoms are aligned, contributing to the overall magnetic behavior of the material.
Robert Klapisch is a French filmmaker, screenwriter, and producer, best known for his work in the film industry. He gained prominence for his films that often explore themes of personal and emotional relationships, as well as the complexities of life.
In mathematics, particularly in set theory and topology, a "polar set" typically refers to a set that is "small" in some sense, often in relation to a particular topology or concept in analysis. The most common usage of the term "polar set" arises in the context of functional analysis and measure theory.
A Schwartz topological vector space is a specific type of topological vector space that is equipped with a topology making it suitable for the analysis of functions and distributions, particularly in the context of functional analysis and distribution theory.
In the context of mathematical analysis and topology, the term "sequentially complete" typically refers to a property of a space that is related to convergence and limits of sequences. A metric space (or more generally, a topological space) is said to be **sequentially complete** if every Cauchy sequence in that space converges to a limit that is also contained within that space.
In mathematics, particularly in the field of harmonic analysis and number theory, a **spectral set** refers to a set of integers that has properties related to the Fourier transform and the theory of sets of integers in relation to frequencies. The precise definition of a spectral set can depend on the context in which it is being used, but a common way to define a spectral set is in relation to its ability to be represented as a set of frequencies of a function or a sequence.
In functional analysis, the concept of a strong dual space is associated with the notion of dual spaces of norms in vector spaces, particularly in the context of locally convex spaces. For a given normed space \(X\), the dual space \(X^*\) is defined as the space of all continuous linear functionals on \(X\).
Symmetric convolution is a specific type of convolution operation that maintains symmetry in its kernel or filter. In general, convolution is a mathematical operation that combines two functions to produce a third function. It is commonly used in signal processing, image processing, and various fields of mathematics and engineering.
Port-Royal Logic refers to a system of logic developed in the 17th century by the philosophers and theologians associated with the Port-Royal Abbey in France, particularly Antoine Arnauld and Claude Lancelot. This logic is most famously articulated in their work "Logique, ou l'Art de penser" (Logic, or the Art of Thinking), published in 1662.
The condition number is a mathematical concept used to measure the sensitivity of the solution of a system of linear equations or an optimization problem to small changes in the input data. It provides insight into how errors or perturbations in the input can affect the output, thus giving a sense of how 'well-conditioned' or 'ill-conditioned' the problem is.
"Antarafacial" and "suprafacial" are terms primarily used in the context of facial treatments and skin care, often relating to techniques involving dermal layers during procedures or analyses. 1. **Antarafacial**: This term typically refers to treatments or techniques that target deeper layers of the skin, such as the dermis and subcutaneous tissue.
An **Archimedean ordered vector space** is a type of vector space equipped with a specific order structure that satisfies certain properties related to the Archimedean property.
In topology, a **Baire space** is a topological space that satisfies a specific property relating to the completeness of the space in a certain sense.
A Banach lattice is a specific type of mathematical structure that arises in functional analysis, which is a branch of mathematics that deals with spaces of functions and their properties. More precisely, a Banach lattice is a combination of two concepts: a Banach space and a lattice. 1. **Banach Space**: A Banach space is a complete normed vector space.
Free probability is a branch of mathematics that studies noncommutative random variables and their relationships, especially in the context of operator algebras and quantum mechanics. It was developed by mathematicians such as Dan Voiculescu in the 1990s and has connections to both probability theory and functional analysis. Here are some key concepts related to free probability: 1. **Free Random Variables**: In free probability, random variables are considered to be "free" in a specific algebraic sense.