Binomial distributionIn probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability ). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.
Multilinear mapIn linear algebra, a multilinear map is a function of several variables that is linear separately in each variable. More precisely, a multilinear map is a function where and are vector spaces (or modules over a commutative ring), with the following property: for each , if all of the variables but are held constant, then is a linear function of . A multilinear map of one variable is a linear map, and of two variables is a bilinear map. More generally, a multilinear map of k variables is called a k-linear map.
Multilinear algebraMultilinear algebra is a branch of mathematics that expands upon the principles of linear algebra. It extends the foundational theory of vector spaces by introducing the concepts of p-vectors and multivectors using Grassmann algebras. In a vector space of dimension n, the focus is primarily on using vectors. However, Hermann Grassmann and others emphasized the importance of considering the structures of pairs, triplets, and general multi-vectors, which offer a more comprehensive perspective.
Poisson distributionIn probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. It is named after French mathematician Siméon Denis Poisson ('pwɑːsɒn; pwasɔ̃). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume.
Space explorationSpace exploration is the use of astronomy and space technology to explore outer space. While the exploration of space is carried out mainly by astronomers with telescopes, its physical exploration is conducted both by uncrewed robotic space probes and human spaceflight. Space exploration, like its classical form astronomy, is one of the main sources for space science. While the observation of objects in space, known as astronomy, predates reliable recorded history, it was the development of large and relatively efficient rockets during the mid-twentieth century that allowed physical space exploration to become a reality.
Marginal distributionIn probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables. This contrasts with a conditional distribution, which gives the probabilities contingent upon the values of the other variables. Marginal variables are those variables in the subset of variables being retained.
Inverse kinematicsIn computer animation and robotics, inverse kinematics is the mathematical process of calculating the variable joint parameters needed to place the end of a kinematic chain, such as a robot manipulator or animation character's skeleton, in a given position and orientation relative to the start of the chain. Given joint parameters, the position and orientation of the chain's end, e.g. the hand of the character or robot, can typically be calculated directly using multiple applications of trigonometric formulas, a process known as forward kinematics.
Exterior algebraIn mathematics, the exterior algebra, or Grassmann algebra, named after Hermann Grassmann, is an algebra that uses the exterior product or wedge product as its multiplication. In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogues. The exterior product of two vectors and , denoted by is called a bivector and lives in a space called the exterior square, a vector space that is distinct from the original space of vectors.
Multilinear formIn abstract algebra and multilinear algebra, a multilinear form on a vector space over a field is a map that is separately -linear in each of its arguments. More generally, one can define multilinear forms on a module over a commutative ring. The rest of this article, however, will only consider multilinear forms on finite-dimensional vector spaces. A multilinear -form on over is called a (covariant) -tensor, and the vector space of such forms is usually denoted or .
Fourier seriesA Fourier series (ˈfʊrieɪ,_-iər) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series, but not all trigonometric series are Fourier series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood. For example, Fourier series were first used by Joseph Fourier to find solutions to the heat equation.
