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The Gram–Schmidt process can be stabilized by a small modification; this version is sometimes referred to as modified Gram-Schmidt or MGS. This approach gives the same result as the original formula in exact arithmetic and introduces smaller errors in finite-precision arithmetic.
1 Gram-Schmidt orthonormalization process. Toggle the table of contents. Wikipedia: Featured picture candidates/Gram-Schmidt orthonormalization ... Download QR code ...
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 .
In linear algebra, the Schmidt decomposition (named after its originator Erhard Schmidt) refers to a particular way of expressing a vector in the tensor product of two inner product spaces. It has numerous applications in quantum information theory , for example in entanglement characterization and in state purification , and plasticity .
2.1.1 Example. 2.1.2 Relation to RQ ... Download as PDF; Printable version; ... Consider the Gram–Schmidt process applied to the columns of the full column rank ...
$ tex Gram-Schmidt_process.tex && dvips -E Gram-Schmidt_process.dvi; Outline fonts $ eps2eps -dNOCACHE Gram-Schmidt_process.ps Gram-Schmidt_process2.eps; Fix bounding box $ ps2epsi Gram-Schmidt_process2.eps Gram-Schmidt_process.eps; Convert to Sketch $ pstoedit -f sk Gram-Schmidt_process.eps Gram-Schmidt_process.sk; Convert to SVG
In geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors.The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product.
An alternative way to arrive at the same expressions is to take the first three derivatives of the curve r′(t), r′′(t), r′′′(t), and to apply the Gram-Schmidt process. The resulting ordered orthonormal basis is precisely the TNB frame. This procedure also generalizes to produce Frenet frames in higher dimensions.