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The first two steps of the Gram–Schmidt process. In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process or Gram-Schmidt algorithm is a way of finding a set of two or more vectors that are perpendicular to each other.
This method has greater numerical stability than the Gram–Schmidt method above. The following table gives the number of operations in the k -th step of the QR-decomposition by the Householder transformation, assuming a square matrix with size n .
A Ziehl–Neelsen stain is an acid-fast stain used to stain species of Mycobacterium tuberculosis that do not stain with the standard laboratory staining procedures such as Gram staining. This stain is performed through the use of both red coloured carbol fuchsin that stains the bacteria and a counter stain such as methylene blue .
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.
The carboxylic acid Schmidt reaction starts with acylium ion 1 obtained from protonation and loss of water. Reaction with hydrazoic acid forms the protonated azido ketone 2 , which goes through a rearrangement reaction with the alkyl group R, migrating over the C-N bond with expulsion of nitrogen.
The Gram matrix is symmetric in the case the inner product is real-valued; it is Hermitian in the general, complex case by definition of an inner product. The Gram matrix is positive semidefinite, and every positive semidefinite matrix is the Gramian matrix for some set of vectors. The fact that the Gramian matrix is positive-semidefinite can ...
The Matlab implementation for the Gram-Schmidt process is for a specific norm and inner product definition (here being the Standard Euclidean Inner Product and by it's extension the 2-norm). Should be updated to reflect that. — Preceding unsigned comment added by BlackMetalStats (talk • contribs) 00:19, 3 April 2017 (UTC)
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