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polar factorization

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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

  • 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

  • List of numerical analysis topics — This is a list of numerical analysis topics, by Wikipedia page. Contents 1 General 2 Error 3 Elementary and special functions 4 Numerical linear algebra …   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

  • 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

  • Motor variable — A function of a motor variable is a function with arguments and values in the split complex number plane, much as functions of a complex variable involve ordinary complex numbers. The split complex numbers lie in the motor plane D, a term… …   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

  • Square root of a matrix — In mathematics, the square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if the matrix product B · B is equal to A.[1] Contents 1 Properties 2 Computation methods …   Wikipedia

  • Logarithm — The graph of the logarithm to base 2 crosses the x axis (horizontal axis) at 1 and passes through the points with coordinates (2, 1), (4, 2), and (8, 3) …   Wikipedia

  • Timeline of Islamic science and engineering — This timeline of Islamic science and engineering covers the general development of science and technology in the Islamic world during the Islamic Golden Age, usually dated from the 7th to 16th centuries.From the 17th century onwards, the advances …   Wikipedia

  • Franck-Condon principle — The Franck Condon principle is a rule in spectroscopy and quantum chemistry that explains the intensity of vibronic transitions. Vibronic transitions are the simultaneous changes in electronic and vibrational energy levels of a molecule due to… …   Wikipedia

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