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In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced / ʃ ə ˈ l ɛ s k i / shə-LES-kee) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations.
In numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix multiplication and matrix decomposition).
Applicable to: square, hermitian, positive definite matrix Decomposition: =, where is upper triangular with real positive diagonal entries Comment: if the matrix is Hermitian and positive semi-definite, then it has a decomposition of the form = if the diagonal entries of are allowed to be zero
Decomposition of strawberries, reverse time lapse African buffalo skull decomposing in the Serengeti National Park, Tanzania A rotten apple after it fell from a tree Decomposing fallen nurse log in a forest
Chemical decomposition, or chemical breakdown, is the process or effect of simplifying a single chemical entity (normal molecule, reaction intermediate, etc.) into two or more fragments. [1]
Top: The action of M, indicated by its effect on the unit disc D and the two canonical unit vectors e 1 and e 2. Left: The action of V ⁎, a rotation, on D, e 1, and e 2. Bottom: The action of Σ, a scaling by the singular values σ 1 horizontally and σ 2 vertically.
Processes in the thermal degradation of organic matter at atmospheric pressure.. Thermal decomposition, or thermolysis, is a chemical decomposition of a substance caused by heat.
This is an important technique for all types of time series analysis, especially for seasonal adjustment. [2] It seeks to construct, from an observed time series, a number of component series (that could be used to reconstruct the original by additions or multiplications) where each of these has a certain characteristic or type of behavior.