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.
Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
The Lovers (1946 film)The Lovers (Amanti in fuga) is a 1946 Italian historical melodrama film directed by Giacomo Gentilomo. It was entered into the 1946 Cannes Film Festival. Gino Bechi as Alessandro Stradella Annette Bach as Ortenzia Foscarini Ernesto Bianchi as Furlan Wanda Capodaglio as Madame Royal Emilio Cigoli Antonio Crast as Marco Foscarini Mario Gallina as Bottesin Kozma Kumani Armando Guarnieri Nino Marchetti Franca Marzi as Porzia Guido Morisi as Il capitano Carlo Ninchi Giovanni Petrucci (as Giovanni Petti) Lamberto
Federico CastellónFederico Castellón ( – ) was a Spanish American painter, sculptor, printmaker, and illustrator of children's books. Castellón was born on Alhabia, Almeria, Spain, studied in Madrid and Paris and settled in Brooklyn, New York. Federico Cristencia de Castellón y Martínez, better known as Federico Castellón, was a surrealist printmaker, illustrator, painter, and sculptor. He was born in Almeria, Spain in 1914. With his family, he immigrated in 1921 to the United States. They resided in Brooklyn, New York.
Runge–Kutta methodsIn numerical analysis, the Runge–Kutta methods (ˈrʊŋəˈkʊtɑː ) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discretization for the approximate solutions of simultaneous nonlinear equations. These methods were developed around 1900 by the German mathematicians Carl Runge and Wilhelm Kutta. The most widely known member of the Runge–Kutta family is generally referred to as "RK4", the "classic Runge–Kutta method" or simply as "the Runge–Kutta method".
Non-inertial reference frameA non-inertial reference frame is a frame of reference that undergoes acceleration with respect to an inertial frame. An accelerometer at rest in a non-inertial frame will, in general, detect a non-zero acceleration. While the laws of motion are the same in all inertial frames, in non-inertial frames, they vary from frame to frame depending on the acceleration. In classical mechanics it is often possible to explain the motion of bodies in non-inertial reference frames by introducing additional fictitious forces (also called inertial forces, pseudo-forces and d'Alembert forces) to Newton's second law.
Linear algebraLinear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.
Kernel (linear algebra)In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the linear subspace of the domain of the map which is mapped to the zero vector. That is, given a linear map L : V → W between two vector spaces V and W, the kernel of L is the vector space of all elements v of V such that L(v) = 0, where 0 denotes the zero vector in W, or more symbolically: The kernel of L is a linear subspace of the domain V.
Rank (linear algebra)In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal number of linearly independent columns of A. This, in turn, is identical to the dimension of the vector space spanned by its rows. Rank is thus a measure of the "nondegenerateness" of the system of linear equations and linear transformation encoded by A. There are multiple equivalent definitions of rank. A matrix's rank is one of its most fundamental characteristics.
Korean mixed scriptKorean mixed script () is a form of writing the Korean language that uses a mixture of the Korean alphabet or Hangul () and Hanja (, ), the Korean name for Chinese characters. The distribution on how to write words usually follows that all native Korean words, including suffixes, particles, and honorific markers are generally written in hangul and never in hanja. Sino-Korean vocabulary or hanja-eo (), either words borrowed from Chinese or created from Sino-Korean roots, were generally always written in hanja, although very rare or complex characters were often substituted with hangul.
Subject–object–verb word orderIn linguistic typology, a subject–object–verb (SOV) language is one in which the subject, object, and verb of a sentence always or usually appear in that order. If English were SOV, "Sam beer drank" would be an ordinary sentence, as opposed to the actual Standard English "Sam drank beer" which is subject–verb–object (SVO). The term is often loosely used for ergative languages like Adyghe and Basque that really have agents instead of subjects.
Linear–quadratic–Gaussian controlIn control theory, the linear–quadratic–Gaussian (LQG) control problem is one of the most fundamental optimal control problems, and it can also be operated repeatedly for model predictive control. It concerns linear systems driven by additive white Gaussian noise. The problem is to determine an output feedback law that is optimal in the sense of minimizing the expected value of a quadratic cost criterion. Output measurements are assumed to be corrupted by Gaussian noise and the initial state, likewise, is assumed to be a Gaussian random vector.
