Eigenvalues and eigenvectorsIn linear algebra, an eigenvector (ˈaɪgənˌvɛktər) or characteristic vector of a linear transformation is a nonzero vector that changes at most by a constant factor when that linear transformation is applied to it. The corresponding eigenvalue, often represented by , is the multiplying factor. Geometrically, a transformation matrix rotates, stretches, or shears the vectors it acts upon. The eigenvectors for a linear transformation matrix are the set of vectors that are only stretched, with no rotation or shear.
Northern HemisphereThe Northern Hemisphere is the half of Earth that is north of the Equator. For other planets in the Solar System, north is defined as being in the same celestial hemisphere relative to the invariable plane of the Solar System as Earth's North Pole. Due to Earth's axial tilt of 23.439281°, winter in the Northern Hemisphere lasts from the December solstice (typically December 21 UTC) to the March equinox (typically March 20 UTC), while summer lasts from the June solstice through to the September equinox (typically on 23 September UTC).
Southern HemisphereThe Southern Hemisphere is the half (hemisphere) of Earth that is south of the Equator. It contains all or parts of five continents (the whole of Antarctica, the whole of Australia, about 90% of South America, about one-third of Africa, and some islands off the continental mainland of Asia) and four oceans (the whole Southern Ocean, the majority of the Indian Ocean, the South Atlantic Ocean, and the South Pacific Ocean), as well as New Zealand and most of the Pacific Islands in Oceania. Its surface is 80.
Western HemisphereThe Western Hemisphere is the half of the planet Earth that lies west of the Prime Meridian (which crosses Greenwich, London, England) and east of the 180th meridian. The other half is called the Eastern Hemisphere. Politically, the term Western Hemisphere is often used as a metonym for the Americas, even though geographically the hemisphere also includes parts of other continents.
Quantum chemistryQuantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions to physical and chemical properties of molecules, materials, and solutions at the atomic level. These calculations include systematically applied approximations intended to make calculations computationally feasible while still capturing as much information about important contributions to the computed wave functions as well as to observable properties such as structures, spectra, and thermodynamic properties.
Prüfer domainIn mathematics, a Prüfer domain is a type of commutative ring that generalizes Dedekind domains in a non-Noetherian context. These rings possess the nice ideal and module theoretic properties of Dedekind domains, but usually only for finitely generated modules. Prüfer domains are named after the German mathematician Heinz Prüfer. The ring of entire functions on the open complex plane form a Prüfer domain. The ring of integer valued polynomials with rational coefficients is a Prüfer domain, although the ring of integer polynomials is not .
Land and water hemispheresThe land hemisphere and water hemisphere are the hemispheres of Earth containing the largest possible total areas of land and ocean, respectively. By definition (assuming that the entire surface can be classed as either "land" or "ocean"), the two hemispheres do not overlap. Determinations of the hemispheres vary slightly. One determination places the centre of the land hemisphere at (in the city of Nantes, France). The centre of the water hemisphere is the antipode of the centre of the land hemisphere, and is therefore located at (near New Zealand's Bounty Islands in the Pacific Ocean).
Eastern HemisphereThe Eastern Hemisphere is the half of the planet Earth which is east of the prime meridian (which crosses Greenwich, London, United Kingdom) and west of the antimeridian (which crosses the Pacific Ocean and relatively little land from pole to pole). It is also used to refer to Afro-Eurasia (Africa and Eurasia) and Australia, in contrast with the Western Hemisphere, which includes mainly North and South America. The Eastern Hemisphere may also be called the "Oriental Hemisphere", and may in addition be used in a cultural or geopolitical sense as a synonym for the "Old World.
