Linear algebraLinear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.
Linear mapIn mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .
Linear combinationIn mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants). The concept of linear combinations is central to linear algebra and related fields of mathematics. Most of this article deals with linear combinations in the context of a vector space over a field, with some generalizations given at the end of the article.
Special linear Lie algebraIn mathematics, the special linear Lie algebra of order n (denoted or ) is the Lie algebra of matrices with trace zero and with the Lie bracket . This algebra is well studied and understood, and is often used as a model for the study of other Lie algebras. The Lie group that it generates is the special linear group. The Lie algebra is central to the study of special relativity, general relativity and supersymmetry: its fundamental representation is the so-called spinor representation, while its adjoint representation generates the Lorentz group SO(3,1) of special relativity.
Linear algebraic groupIn mathematics, a linear algebraic group is a subgroup of the group of invertible matrices (under matrix multiplication) that is defined by polynomial equations. An example is the orthogonal group, defined by the relation where is the transpose of . Many Lie groups can be viewed as linear algebraic groups over the field of real or complex numbers. (For example, every compact Lie group can be regarded as a linear algebraic group over R (necessarily R-anisotropic and reductive), as can many noncompact groups such as the simple Lie group SL(n,R).
MathematicsMathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them.
Applied mathematicsApplied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models.
GenderGender includes the social, psychological, cultural and behavioral aspects of being a man, woman, or other gender identity. Depending on the context, this may include sex-based social structures (i.e. gender roles) and gender expression. Most cultures use a gender binary, in which gender is divided into two categories, and people are considered part of one or the other (boys/men and girls/women); those who are outside these groups may fall under the umbrella term non-binary.
Gender roleA gender role, also known as a sex role, is a social role encompassing a range of behaviors and attitudes that are generally considered acceptable, appropriate, or desirable for a person based on that person's sex. Gender roles are usually centered on conceptions of masculinity and femininity, although there are exceptions and variations. The specifics regarding these gendered expectations may vary among cultures, while other characteristics may be common throughout a range of cultures.
Gender varianceGender variance or gender nonconformity is behavior or gender expression by an individual that does not match masculine or feminine gender norms. A gender-nonconforming person may be variant in their gender identity, being transgender or non-binary, or they may be cisgender. In the case of transgender people, they may be perceived, or perceive themselves as, gender-nonconforming before transitioning, but might not be perceived as such after transitioning.
Gender identityGender identity is the personal sense of one's own gender. Gender identity can correlate with a person's assigned sex or can differ from it. In most individuals, the various biological determinants of sex are congruent, and consistent with the individual's gender identity. Gender expression typically reflects a person's gender identity, but this is not always the case. While a person may express behaviors, attitudes, and appearances consistent with a particular gender role, such expression may not necessarily reflect their gender identity.
École polytechniqueÉcole polytechnique, also known as Polytechnique or l'X liks, is a grande école located in Palaiseau, France. It specializes in science and engineering and is a founding member of the Polytechnic Institute of Paris. The school was founded in 1794 by mathematician Gaspard Monge during the French Revolution and was militarized under Napoleon I in 1804. It is still supervised by the French Ministry of Armed Forces. Originally located in the Latin Quarter in central Paris, the institution moved to Palaiseau in 1976, in the Paris-Saclay technology cluster.
Gender dysphoriaGender dysphoria (GD) is the distress a person experiences due to a mismatch between their gender identitytheir personal sense of their own genderand their sex assigned at birth. Previously, the diagnostic label gender identity disorder (GID) was used, until it was eliminated in 2013 with the release of the diagnostic manual DSM-5 in favor of the current term. The condition was renamed to remove the stigma associated with the term disorder. People with gender dysphoria commonly identify as transgender.
Gender neutralityGender neutrality (adjective form: gender-neutral), also known as gender-neutralism or the gender neutrality movement, is the idea that policies, language, and other social institutions (social structures or gender roles) should avoid distinguishing roles according to people's sex or gender. This is in order to avoid discrimination arising from the impression that there are social roles for which one gender is more suited than another.
Gender studiesGender studies is an interdisciplinary academic field devoted to analysing gender identity and gendered representation. Gender studies originated in the field of women's studies, concerning women, feminism, gender, and politics. The field now overlaps with queer studies and men's studies. Its rise to prominence, especially in Western universities after 1990, coincided with the rise of deconstruction.
Gender systemGender systems are the social structures that establish the number of genders and their associated gender roles in every society. A gender role is "everything that a person says and does to indicate to others or to the self the degree that one is either male, female, or androgynous. This includes but is not limited to sexual and erotic arousal and response." Gender identity is one's own personal experience with gender role and the persistence of one's individuality as male, female, or androgynous, especially in self-awareness and behavior.
Grande écoleA grande école (ɡʁɑ̃d ekɔl; great school) is a specialized top level educational institution in France. Grandes écoles are part of an alternative educational system that operates alongside the mainstream French public university system and are dedicated to teaching, research and professional training in single academic fields such as engineering, architecture, business administration, academic research, or public policy and administration.
Social classA social class or social stratum is a grouping of people into a set of hierarchical social categories, the most common being the upper, middle and lower classes. Membership in a social class can for example be dependent on education, wealth, occupation, income, and belonging to a particular subculture or social network. "Class" is a subject of analysis for sociologists, political scientists, anthropologists and social historians. The term has a wide range of sometimes conflicting meanings, and there is no broad consensus on a definition of "class".
Middle classThe middle class refers to a class of people in the middle of a social hierarchy, often defined by occupation, income, education, or social status. The term has historically been associated with modernity, capitalism and political debate. Common definitions for the middle class range from the middle fifth of individuals on a nation's income ladder, to everyone but the poorest and wealthiest 20%. Theories like "Paradox of Interest" use decile groups and wealth distribution data to determine the size and wealth share of the middle class.
Confidence intervalIn frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used. The confidence level, degree of confidence or confidence coefficient represents the long-run proportion of CIs (at the given confidence level) that theoretically contain the true value of the parameter; this is tantamount to the nominal coverage probability.
