Projection (mathematics)In mathematics, a projection is an idempotent mapping of a set (or other mathematical structure) into a subset (or sub-structure). In this case, idempotent means that projecting twice is the same as projecting once. The restriction to a subspace of a projection is also called a projection, even if the idempotence property is lost. An everyday example of a projection is the casting of shadows onto a plane (sheet of paper): the projection of a point is its shadow on the sheet of paper, and the projection (shadow) of a point on the sheet of paper is that point itself (idempotency).
Spectrum (functional analysis)In mathematics, particularly in functional analysis, the spectrum of a bounded linear operator (or, more generally, an unbounded linear operator) is a generalisation of the set of eigenvalues of a matrix. Specifically, a complex number is said to be in the spectrum of a bounded linear operator if either has no set-theoretic inverse; or the set-theoretic inverse is either unbounded or defined on a non-dense subset. Here, is the identity operator. By the closed graph theorem, is in the spectrum if and only if the bounded operator is non-bijective on .
Sign languageSign languages (also known as signed languages) are languages that use the visual-manual modality to convey meaning, instead of spoken words. Sign languages are expressed through manual articulation in combination with non-manual markers. Sign languages are full-fledged natural languages with their own grammar and lexicon. Sign languages are not universal and are usually not mutually intelligible, although there are also similarities among different sign languages.
British Sign LanguageBritish Sign Language (BSL) is a sign language used in the United Kingdom and is the first or preferred language among the deaf community in the UK. Based on the percentage of people who reported 'using British Sign Language at home' on the 2011 Scottish Census, the British Deaf Association estimates there are 151,000 BSL users in the UK, of whom 87,000 are Deaf. By contrast, in the 2011 England and Wales Census 15,000 people living in England and Wales reported themselves using BSL as their main language.
Diagonal matrixIn linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is , while an example of a 3×3 diagonal matrix is. An identity matrix of any size, or any multiple of it (a scalar matrix), is a diagonal matrix. A diagonal matrix is sometimes called a scaling matrix, since matrix multiplication with it results in changing scale (size).
Matrix decompositionIn the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems. In numerical analysis, different decompositions are used to implement efficient matrix algorithms. For instance, when solving a system of linear equations , the matrix A can be decomposed via the LU decomposition.
GLI1Zinc finger protein GLI1 also known as glioma-associated oncogene is a protein that in humans is encoded by the GLI1 gene. It was originally isolated from human glioblastoma cells. The Gli proteins are the effectors of Hedgehog (Hh) signaling and have been shown to be involved in cell fate determination, proliferation and patterning in many cell types and most organs during embryo development.
GLI3Zinc finger protein GLI3 is a protein that in humans is encoded by the GLI3 gene. This gene encodes a protein that belongs to the C2H2-type zinc finger proteins subclass of the Gli family. They are characterized as DNA-binding transcription factors and are mediators of Sonic hedgehog (Shh) signaling. The protein encoded by this gene localizes in the cytoplasm and activates patched Drosophila homolog (PTCH1) gene expression. It is also thought to play a role during embryogenesis.
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).
Isle of Man TTThe Isle of Man TT or Tourist Trophy races are an annual motorcycle racing event run on the Isle of Man in May/June of most years since its inaugural race in 1907. The event is often called one of the most dangerous racing events in the world as many competitors have died. The Isle of Man TT is run in a time-trial format on public roads closed to the public by an Act of Tynwald. The event consists of one week of practice and qualifying sessions followed by one week of racing.
GLI2Zinc finger protein GLI2 also known as GLI family zinc finger 2 is a protein that in humans is encoded by the GLI2 gene. The protein encoded by this gene is a transcription factor. GLI2 belongs to the C2H2-type zinc finger protein subclass of the Gli family. Members of this subclass are characterized as transcription factors which bind DNA through zinc finger motifs. These motifs contain conserved H-C links. Gli family zinc finger proteins are mediators of Sonic hedgehog (Shh) signaling and they are implicated as potent oncogenes in the embryonal carcinoma cell.
Cross productIn mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here ), and is denoted by the symbol . Given two linearly independent vectors a and b, the cross product, a × b (read "a cross b"), is a vector that is perpendicular to both a and b, and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming.
