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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 Gram matrix of a sequence of points ,, …, in k-dimensional space ℝ k is the n×n matrix = of their dot products (here a point is thought of as a vector from 0 to that point):
The matrix G is the usual Gram matrix of a set of vectors, derived from the set of rows of R, while G′ is the Gram matrix derived from the set of columns of R. A matrix R for which G = G′ is a normal matrix. Every known maximal-determinant matrix is equivalent to a normal matrix, but it is not known whether this is always the case.
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.
Matrix theory is the branch of mathematics that focuses on the study of matrices. ... Gram–Schmidt process – Orthonormalization of a set of vectors;
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What to know about Sens. John Thune, John Cornyn, and Rick Scott as they run to replace Mitch McConnell in the top GOP leadership spot.
The RQ decomposition transforms a matrix A into the product of an upper triangular matrix R (also known as right-triangular) and an orthogonal matrix Q. The only difference from QR decomposition is the order of these matrices. QR decomposition is Gram–Schmidt orthogonalization of columns of A, started from the first column.