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

Simon's Algorithm - Problem Description and Algorithm

... The set of n-bit strings is a

... 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

... 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

... 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

... 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

... 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)