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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.
Advanced Placement (AP) United States Government and Politics (often shortened to AP Gov or AP GoPo and sometimes referred to as AP American Government or simply AP Government) is a college-level course and examination offered to high school students through the College Board's Advanced Placement Program.
A key feature of the necessary field is ... decay width of 4.07 × 10 −3 GeV. [2] ... title of the 1993 book on the Higgs boson and particle physics, ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
The oldest known mathematics textbook is the Rhind papyrus, dated from c. 1650 BCE in Egypt. [184] Due to a scarcity of books, mathematical teachings in ancient India were communicated using memorized oral tradition since the Vedic period (c. 1500 – c. 500 BCE). [185]
Elements of H 2 (g, F) are equivalence classes of 2-cocycles and two 2-cocycles φ 1 and φ 2 are called equivalent cocycles if they differ by a 2-coboundary, i.e. if φ 1 = φ 2 + δf for some f ∈ C 1 (g, F). Equivalent 2-cocycles are called cohomologous. The equivalence class of φ ∈ Z 2 (g, F) is denoted [φ] ∈ H 2. These notions ...