Defective matrixIn linear algebra, a defective matrix is a square matrix that does not have a complete basis of eigenvectors, and is therefore not diagonalizable. In particular, an n × n matrix is defective if and only if it does not have n linearly independent eigenvectors. A complete basis is formed by augmenting the eigenvectors with generalized eigenvectors, which are necessary for solving defective systems of ordinary differential equations and other problems.
Eigendecomposition of a matrixIn linear algebra, eigendecomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Only diagonalizable matrices can be factorized in this way. When the matrix being factorized is a normal or real symmetric matrix, the decomposition is called "spectral decomposition", derived from the spectral theorem. Eigenvalue, eigenvector and eigenspace A (nonzero) vector v of dimension N is an eigenvector of a square N × N matrix A if it satisfies a linear equation of the form for some scalar λ.
CentralityIn graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, super-spreaders of disease, and brain networks. Centrality concepts were first developed in social network analysis, and many of the terms used to measure centrality reflect their sociological origin.
Dutch languageDutch (Nederlands ˈneːdərlɑnts), also known as Netherlandic or Netherlandish, is a West Germanic language spoken by about 25 million people as a first language and 5 million as a second language. It is the third most widely spoken Germanic language, after its close relatives German and English. Afrikaans is a separate but somewhat mutually intelligible daughter language spoken, to some degree, by at least 16 million people, mainly in South Africa and Namibia, evolving from the Cape Dutch dialects of Southern Africa.
Proof by contradictionIn logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally valid. More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved.
ThiolIn organic chemistry, a thiol ('θaɪɒl; ), or thiol derivative, is any organosulfur compound of the form , where R represents an alkyl or other organic substituent. The functional group itself is referred to as either a thiol group or a sulfhydryl group, or a sulfanyl group. Thiols are the sulfur analogue of alcohols (that is, sulfur takes the place of oxygen in the hydroxyl () group of an alcohol), and the word is a blend of "thio-" with "alcohol". Many thiols have strong odors resembling that of garlic or rotten eggs.
AfrikaansAfrikaans (UKˌæfrᵻˈkɑːns, USˌɑːf-) is a West Germanic language that evolved in the Dutch Cape Colony from the Dutch vernacular of Holland proper (i.e., the Hollandic dialect) used by Dutch, French, and German settlers and people enslaved by them. Afrikaans gradually began to develop distinguishing characteristics during the course of the 18th century. Now spoken in South Africa, Namibia and (to a lesser extent) Botswana, Zambia and Zimbabwe, estimates 2010 of the total number of Afrikaans speakers range between 15 and 23 million.
Null graphIn the mathematical field of graph theory, the term "null graph" may refer either to the order-zero graph, or alternatively, to any edgeless graph (the latter is sometimes called an "empty graph"). The order-zero graph, K_0, is the unique graph having no vertices (hence its order is zero). It follows that K_0 also has no edges. Thus the null graph is a regular graph of degree zero. Some authors exclude K_0 from consideration as a graph (either by definition, or more simply as a matter of convenience).
LuxembourgishLuxembourgish (ˈlʌksəmbɜːrɡɪʃ ; also Luxemburgish, Luxembourgian, Letzebu(e)rgesch; Luxembourgish: Lëtzebuergesch ˈlətsəbuəjəʃ) is a West Germanic language that is spoken mainly in Luxembourg. About 400,000 people speak Luxembourgish worldwide. As a standard form of the Moselle Franconian language, Luxembourgish has similarities with other varieties of High German and the wider group of West Germanic languages.
Germanic strong verbIn the Germanic languages, a strong verb is a verb that marks its past tense by means of changes to the stem vowel. The majority of the remaining verbs form the past tense by means of a dental suffix, and are known as weak verbs. In modern English, strong verbs include sing (present I sing, past I sang, past participle I have sung) and drive (present I drive, past I drove, past participle I have driven), as opposed to weak verbs such as open (present I open, past I opened, past participle I have opened).
Directed graphIn mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs. In formal terms, a directed graph is an ordered pair where V is a set whose elements are called vertices, nodes, or points; A is a set of ordered pairs of vertices, called arcs, directed edges (sometimes simply edges with the corresponding set named E instead of A), arrows, or directed lines.
Lattice graphIn graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space \mathbb{R}^n, forms a regular tiling. This implies that the group of bijective transformations that send the graph to itself is a lattice in the group-theoretical sense. Typically, no clear distinction is made between such a graph in the more abstract sense of graph theory, and its drawing in space (often the plane or 3D space). This type of graph may more shortly be called just a lattice, mesh, or grid.
