- polar decomposition
- мат. полярное разложение
Большой англо-русский и русско-английский словарь. 2001.
polar decomposition
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Polar decomposition — In mathematics, particularly in linear algebra and functional analysis, the polar decomposition of a matrix or linear operator is a factorization analogous to the polar form of a nonzero complex number z where r is the absolute value of z (a… … Wikipedia
polar ecosystem — Introduction complex of living organisms in polar regions such as polar barrens and tundra. Polar barrens and tundra are found at high latitudes on land surfaces not covered by perpetual ice and snow. These areas lying beyond the tree line … Universalium
Singular value decomposition — Visualization of the SVD of a 2 dimensional, real shearing matrix M. First, we see the unit disc in blue together with the two canonical unit vectors. We then see the action of M, which distorts the disk to an ellipse. The SVD decomposes M into… … Wikipedia
Cartan decomposition — The Cartan decomposition is a decomposition of a semisimple Lie group or Lie algebra, which plays an important role in their structure theory and representation theory. It generalizes the polar decomposition of matrices. Cartan involutions on Lie … Wikipedia
Matrix decomposition — In the mathematical discipline of linear algebra, a matrix decomposition is a factorization of a matrix into some canonical form. There are many different matrix decompositions; each finds use among a particular class of problems. Contents 1… … Wikipedia
QR decomposition — In linear algebra, the QR decomposition (also called the QR factorization) of a matrix is a decomposition of the matrix into an orthogonal and a right triangular matrix. The QR decomposition is often used to solve the linear least squares problem … Wikipedia
Lie group decomposition — In mathematics, Lie group decompositions are used to analyse the structure of Lie groups and associated objects, by showing how they are built up out of subgroups. They are essential technical tools in the representation theory of Lie groups and… … Wikipedia
Vector decomposition — refers to decomposing a vector of Rn into several vectors, each linearly independent (in mutually distinct directions in the n dimensional space). Vector decomposition in two dimensions In two dimensions, a vector can be decomposed in many ways.… … Wikipedia
Orthogonal matrix — In linear algebra, an orthogonal matrix (less commonly called orthonormal matrix[1]), is a square matrix with real entries whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors). Equivalently, a matrix Q is orthogonal if… … Wikipedia
Rotation matrix — In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For example the matrix rotates points in the xy Cartesian plane counterclockwise through an angle θ about the origin of the Cartesian… … Wikipedia
List of mathematics articles (P) — NOTOC P P = NP problem P adic analysis P adic number P adic order P compact group P group P² irreducible P Laplacian P matrix P rep P value P vector P y method Pacific Journal of Mathematics Package merge algorithm Packed storage matrix Packing… … Wikipedia
