# Basis Vectors

### Some articles on vector, basis vectors, basis, vectors:

Simon's Algorithm - Problem Description and Algorithm
... The set of n-bit strings is a vector space under bitwise XOR ... Using quantum algorithms, we can, with arbitrarily high probability determine the basis vectors spanning this n-1 subspace since s is a vector orthogonal to all of the basis vectors ... Given enough samples of y, we can figure out the n-1 basis vectors, and compute s ...
Orthogonal Curvilinear Coordinates in 3d - Coordinates, Basis, and Vectors
... coordinates is given by the invertible transformations Any point can be written as a position vector r in either coordinate system ... where x, y, z are the coordinates of the position vector with respect to the basis vectors ex, ey, ez ... The Cartesian basis vectors are the standard basis set of vectors ...
Signal Subspace
... Such samples can be viewed as vectors in a high-dimensional vector space over the real numbers ... PCA is used to identify a set of orthogonal basis vectors (basis signals) which capture as much as possible of the energy in the ensemble of observed samples ... The vector space spanned by the basis vectors identified by the analysis is then the signal subspace ...
Orthogonal Curvilinear Coordinates in 3d - Covariant and Contravariant Bases
... The basis vectors, gradients, and scale factors are all interrelated within a coordinate system by two methods the basis vectors are unit tangent vectors along the coordinate curves which ... by which they are built, for a general curvilinear coordinate system there are two sets of basis vectors for every point {b1, b2, b3} is the covariant basis, and {b1, b2, b3} is the ... A vector v can be given in terms either basis, i.e ...
Crystal Base - Definition
... In an integrable module, and for weight, a vector (i.e ... a vector in with weight ) can be uniquely decomposed into the sums where, only if, and only if ... such that is a free -submodule of such that is a -basis of the vector space over and, where and and and To put this into a more informal setting, the actions of ...

### Famous quotes containing the word basis:

Even upon such a basis hast thou built
A monument, whose cement hath been guilt!
George Gordon Noel Byron (1788–1824)