TransposeIn linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by AT (among other notations). The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley. In the case of a logical matrix representing a binary relation R, the transpose corresponds to the converse relation RT.
Newton's methodIn numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a single-variable function f defined for a real variable x, the function's derivative f′, and an initial guess x0 for a root of f. If the function satisfies sufficient assumptions and the initial guess is close, then is a better approximation of the root than x0.
Vandermonde matrixIn linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row: an matrix with entries , the jth power of the number , for all zero-based indices and . Most authors define the Vandermonde matrix as the transpose of the above matrix. The determinant of a square Vandermonde matrix (when ) is called a Vandermonde determinant or Vandermonde polynomial. Its value is: This is non-zero if and only if all are distinct (no two are equal), making the Vandermonde matrix invertible.
Circulant matrixIn linear algebra, a circulant matrix is a square matrix in which all row vectors are composed of the same elements and each row vector is rotated one element to the right relative to the preceding row vector. It is a particular kind of Toeplitz matrix. In numerical analysis, circulant matrices are important because they are diagonalized by a discrete Fourier transform, and hence linear equations that contain them may be quickly solved using a fast Fourier transform.
Hyperbaric medicineHyperbaric medicine is medical treatment in which an ambient pressure greater than sea level atmospheric pressure is a necessary component. The treatment comprises hyperbaric oxygen therapy (HBOT), the medical use of oxygen at an ambient pressure higher than atmospheric pressure, and therapeutic recompression for decompression illness, intended to reduce the injurious effects of systemic gas bubbles by physically reducing their size and providing improved conditions for elimination of bubbles and excess dissolved gas.
Diving medicineDiving medicine, also called undersea and hyperbaric medicine (UHB), is the diagnosis, treatment and prevention of conditions caused by humans entering the undersea environment. It includes the effects on the body of pressure on gases, the diagnosis and treatment of conditions caused by marine hazards and how relationships of a diver's fitness to dive affect a diver's safety. Diving medical practitioners are also expected to be competent in the examination of divers and potential divers to determine fitness to dive.
