# Basis Vectors

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

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 transform like covariant ... 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 contravariant basis ... A vector v can be given in terms either basis, i.e ...
Orthogonal Curvilinear Coordinates in 3d - Coordinates, Basis, and Vectors
... 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 ...
Simon's Algorithm - Problem Description and Algorithm
... The set of n-bit strings is a vector space under bitwise XOR ... 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 ...
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 ... pair, 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 ...

### Famous quotes containing the word basis:

The basis of good manners is self-reliance. Necessity is the law of all who are not self-possessed.
Ralph Waldo Emerson (1803–1882)