Geometric algebraIn mathematics, a geometric algebra (also known as a real Clifford algebra) is an extension of elementary algebra to work with geometrical objects such as vectors. Geometric algebra is built out of two fundamental operations, addition and the geometric product. Multiplication of vectors results in higher-dimensional objects called multivectors. Compared to other formalisms for manipulating geometric objects, geometric algebra is noteworthy for supporting vector division and addition of objects of different dimensions.
Matrix multiplication algorithmBecause matrix multiplication is such a central operation in many numerical algorithms, much work has been invested in making matrix multiplication algorithms efficient. Applications of matrix multiplication in computational problems are found in many fields including scientific computing and pattern recognition and in seemingly unrelated problems such as counting the paths through a graph. Many different algorithms have been designed for multiplying matrices on different types of hardware, including parallel and distributed systems, where the computational work is spread over multiple processors (perhaps over a network).
High-definition televisionHigh-definition television (HD or HDTV) describes a television system which provides a substantially higher than the previous generation of technologies. The term has been used since 1936; in more recent times, it refers to the generation following standard-definition television (SDTV), often abbreviated to HDTV or HD-TV. It is the current de facto standard video format used in most broadcasts: terrestrial broadcast television, cable television, satellite television and Blu-ray Discs.
École polytechniqueÉcole polytechnique, also known as Polytechnique or l'X liks, is a grande école located in Palaiseau, France. It specializes in science and engineering and is a founding member of the Polytechnic Institute of Paris. The school was founded in 1794 by mathematician Gaspard Monge during the French Revolution and was militarized under Napoleon I in 1804. It is still supervised by the French Ministry of Armed Forces. Originally located in the Latin Quarter in central Paris, the institution moved to Palaiseau in 1976, in the Paris-Saclay technology cluster.
Direction findingDirection finding (DF), or radio direction finding (RDF), is - in accordance with International Telecommunication Union (ITU) - defined as radio location that uses the reception of radio waves to determine the direction in which a radio station or an object is located. This can refer to radio or other forms of wireless communication, including radar signals detection and monitoring (ELINT/ESM). By combining the direction information from two or more suitably spaced receivers (or a single mobile receiver), the source of a transmission may be located via triangulation.
High-definition videoHigh-definition video (HD video) is video of higher resolution and quality than standard-definition. While there is no standardized meaning for high-definition, generally any video image with considerably more than 480 vertical scan lines (North America) or 576 vertical lines (Europe) is considered high-definition. 480 scan lines is generally the minimum even though the majority of systems greatly exceed that. Images of standard resolution captured at rates faster than normal (60 frames/second North America, 50 fps Europe), by a high-speed camera may be considered high-definition in some contexts.
Vector processorIn computing, a vector processor or array processor is a central processing unit (CPU) that implements an instruction set where its instructions are designed to operate efficiently and effectively on large one-dimensional arrays of data called vectors. This is in contrast to scalar processors, whose instructions operate on single data items only, and in contrast to some of those same scalar processors having additional single instruction, multiple data (SIMD) or SWAR Arithmetic Units.
Grande écoleA grande école (ɡʁɑ̃d ekɔl; great school) is a specialized top level educational institution in France. Grandes écoles are part of an alternative educational system that operates alongside the mainstream French public university system and are dedicated to teaching, research and professional training in single academic fields such as engineering, architecture, business administration, academic research, or public policy and administration.
Automatic vectorizationAutomatic vectorization, in parallel computing, is a special case of automatic parallelization, where a computer program is converted from a scalar implementation, which processes a single pair of operands at a time, to a vector implementation, which processes one operation on multiple pairs of operands at once. For example, modern conventional computers, including specialized supercomputers, typically have vector operations that simultaneously perform operations such as the following four additions (via SIMD or SPMD hardware): However, in most programming languages one typically writes loops that sequentially perform additions of many numbers.
Melting pointThe melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends on pressure and is usually specified at a standard pressure such as 1 atmosphere or 100 kPa. When considered as the temperature of the reverse change from liquid to solid, it is referred to as the freezing point or crystallization point.
Point (geometry)In classical Euclidean geometry, a point is a primitive notion that models an exact location in space, and has no length, width, or thickness. In modern mathematics, a point refers more generally to an element of some set called a space. Being a primitive notion means that a point cannot be defined in terms of previously defined objects. That is, a point is defined only by some properties, called axioms, that it must satisfy; for example, "there is exactly one line that passes through two different points".
Accumulation pointIn mathematics, a limit point, accumulation point, or cluster point of a set in a topological space is a point that can be "approximated" by points of in the sense that every neighbourhood of with respect to the topology on also contains a point of other than itself. A limit point of a set does not itself have to be an element of There is also a closely related concept for sequences.
