Vector spaceIn mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied ("scaled") by numbers called scalars. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. The terms real vector space and complex vector space are often used to specify the nature of the scalars: real coordinate space or complex coordinate space.
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.
Trace (linear algebra)In linear algebra, the trace of a square matrix A, denoted tr(A), is defined to be the sum of elements on the main diagonal (from the upper left to the lower right) of A. The trace is only defined for a square matrix (n × n). It can be proven that the trace of a matrix is the sum of its (complex) eigenvalues (counted with multiplicities). It can also be proven that tr(AB) = tr(BA) for any two matrices A and B. This implies that similar matrices have the same trace.
Mean value theoremIn mathematics, the mean value theorem (or Lagrange theorem) states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints. It is one of the most important results in real analysis. This theorem is used to prove statements about a function on an interval starting from local hypotheses about derivatives at points of the interval.
Rolle's theoremIn calculus, Rolle's theorem or Rolle's lemma essentially states that any real-valued differentiable function that attains equal values at two distinct points must have at least one stationary point somewhere between them—that is, a point where the first derivative (the slope of the tangent line to the graph of the function) is zero. The theorem is named after Michel Rolle.
Compact spaceIn mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it includes all limiting values of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval [0,1] would be compact.
EmailElectronic mail (email or e-mail) is a method of transmitting and receiving messages using electronic devices. It was conceived in the late–20th century as the digital version of, or counterpart to, mail (hence e- + mail). Email is a ubiquitous and very widely used communication medium; in current use, an email address is often treated as a basic and necessary part of many processes in business, commerce, government, education, entertainment, and other spheres of daily life in most countries.
Mon peopleThe Mon (ဂကူမန်;(Thai Mon=ဂကူမည်); မွန်လူမျိုး, mʊ̀ɰ̃ lù mjó; มอญ, mɔ̄ːn ) are an ethnic group who inhabit Lower Myanmar's Mon State, Kayin State, Kayah State, Tanintharyi Region, Bago Region, the Irrawaddy Delta, and several areas in Thailand (mostly in Pathum Thani province, Phra Pradaeng and Nong Ya Plong). The native language is Mon, which belongs to the Monic branch of the Austroasiatic language family and shares a common origin with the Nyah Kur language, which is spoken by the people of the same name that live in Northeastern Thailand.
Email spamEmail spam, also referred to as junk email, spam mail, or simply spam, is unsolicited messages sent in bulk by email (spamming). The name comes from a Monty Python sketch in which the name of the canned pork product Spam is ubiquitous, unavoidable, and repetitive. Email spam has steadily grown since the early 1990s, and by 2014 was estimated to account for around 90% of total email traffic. Since the expense of the spam is borne mostly by the recipient, it is effectively postage due advertising.
Dot productIn mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or rarely projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see Inner product space for more).
Email addressAn email address identifies an email box to which messages are delivered. While early messaging systems used a variety of formats for addressing, today, email addresses follow a set of specific rules originally standardized by the Internet Engineering Task Force (IETF) in the 1980s, and updated by . The term email address in this article refers to just the addr-spec in Section 3.4 of RFC 5322. The RFC defines address more broadly as either a mailbox or group.
Mailing listA mailing list is a collection of names and addresses used by an individual or an organization to send material to multiple recipients. The term is often extended to include the people subscribed to such a list, so the group of subscribers is referred to as "the mailing list", or simply "the list." Transmission may be paper-based or electronic. Each has its strengths, although a 2022 article claimed that "direct mail still brings in the lion's share of revenue for most organizations.
