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The calculation of the sequence , …, is known as Gram–Schmidt orthogonalization, and the calculation of the sequence , …, is known as Gram–Schmidt orthonormalization. To check that these formulas yield an orthogonal sequence, first compute u 1 , u 2 {\displaystyle \langle \mathbf {u} _{1},\mathbf {u} _{2}\rangle } by substituting the ...
[1] [2] [3] It is named after Karl Friedrich Schmidt (1887–1971), who first reported it in 1924 by successfully converting benzophenone and hydrazoic acid to benzanilide. [4] The intramolecular reaction was not reported until 1991 [5] but has become important in the synthesis of natural products. [6]
In numerical linear algebra, the Arnoldi iteration is an eigenvalue algorithm and an important example of an iterative method.Arnoldi finds an approximation to the eigenvalues and eigenvectors of general (possibly non-Hermitian) matrices by constructing an orthonormal basis of the Krylov subspace, which makes it particularly useful when dealing with large sparse matrices.
Jørgen Pedersen Gram (27 June 1850 – 29 April 1916) was a Danish actuary and mathematician who was born in Nustrup, Duchy of Schleswig, Denmark and died in Copenhagen, Denmark. Important papers of his include On series expansions determined by the methods of least squares , and Investigations of the number of primes less than a given number .
The following other wikis use this file: Usage on bs.wikipedia.org Gram–Schmidtov postupak; Usage on ca.wikipedia.org Procés d'ortogonalització de Gram-Schmidt
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This reaction is named after two of its pioneering investigators Rainer Ludwig Claisen and J. Gustav Schmidt, who independently published on this topic in 1880 and 1881. [ 1 ] [ 2 ] [ 3 ] An example is the synthesis of dibenzylideneacetone ((1 E , 4 E )-1,5-diphenylpenta-1,4-dien-3-one).
Erhard Schmidt (13 January 1876 – 6 December 1959) was a Baltic German mathematician whose work significantly influenced the direction of mathematics in the twentieth century. [2] Schmidt was born in Tartu (German: Dorpat ), in the Governorate of Livonia (now Estonia ).