Transformation matrixIn linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . Note that has rows and columns, whereas the transformation is from to . There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Matrices allow arbitrary linear transformations to be displayed in a consistent format, suitable for computation.
Quechuan languagesQuechua (ˈkɛtʃuə, ˈkɛtʃwɑː; ˈketʃwa), usually called Runasimi ("people's language") in Quechuan languages, is an indigenous language family spoken by the Quechua peoples, primarily living in the Peruvian Andes. Derived from a common ancestral language, it is the most widely spoken pre-Columbian language family of the Americas, with an estimated 8–10 million speakers as of 2004. Approximately 25% (7.7 million) of Peruvians speak a Quechuan language. Quechua was the main language family of the Inca Empire.
Shear mappingIn plane geometry, a shear mapping is a linear map that displaces each point in a fixed direction, by an amount proportional to its signed distance from the line that is parallel to that direction and goes through the origin. This type of mapping is also called shear transformation, transvection, or just shearing. An example is the mapping that takes any point with coordinates to the point . In this case, the displacement is horizontal by a factor of 2 where the fixed line is the x-axis, and the signed distance is the y-coordinate.
Word orderIn linguistics, word order (also known as linear order) is the order of the syntactic constituents of a language. Word order typology studies it from a cross-linguistic perspective, and examines how different languages employ different orders. Correlations between orders found in different syntactic sub-domains are also of interest. The primary word orders that are of interest are the constituent order of a clause, namely the relative order of subject, object, and verb; the order of modifiers (adjectives, numerals, demonstratives, possessives, and adjuncts) in a noun phrase; the order of adverbials.
Semantic similaritySemantic similarity is a metric defined over a set of documents or terms, where the idea of distance between items is based on the likeness of their meaning or semantic content as opposed to lexicographical similarity. These are mathematical tools used to estimate the strength of the semantic relationship between units of language, concepts or instances, through a numerical description obtained according to the comparison of information supporting their meaning or describing their nature.
Entity linkingIn natural language processing, entity linking, also referred to as named-entity linking (NEL), named-entity disambiguation (NED), named-entity recognition and disambiguation (NERD) or named-entity normalization (NEN) is the task of assigning a unique identity to entities (such as famous individuals, locations, or companies) mentioned in text. For example, given the sentence "Paris is the capital of France", the idea is to determine that "Paris" refers to the city of Paris and not to Paris Hilton or any other entity that could be referred to as "Paris".
Generative artificial intelligenceGenerative artificial intelligence (AI) is artificial intelligence capable of generating text, images, or other media, using generative models. Generative AI models learn the patterns and structure of their input training data and then generate new data that has similar characteristics. In the early 2020s, advances in transformer-based deep neural networks enabled a number of generative AI systems notable for accepting natural language prompts as input.
Invertible matrixIn linear algebra, an n-by-n square matrix A is called invertible (also nonsingular, nondegenerate or (rarely used) regular), if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A−1. Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.
Khoisan languagesThe Khoisan languages (ˈkɔɪsɑːn ; also Khoesan or Khoesaan) are a number of African languages once classified together, originally by Joseph Greenberg. Khoisan is defined as those languages that have click consonants and do not belong to other African language families. For much of the 20th century, they were thought to be genealogically related to each other, but this is no longer accepted. They are now held to comprise three distinct language families and two language isolates.
Block matrixIn mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices. Intuitively, a matrix interpreted as a block matrix can be visualized as the original matrix with a collection of horizontal and vertical lines, which break it up, or partition it, into a collection of smaller matrices. Any matrix may be interpreted as a block matrix in one or more ways, with each interpretation defined by how its rows and columns are partitioned.
