Basis Class

public class Basis

Public Class Basis

public ref class Basis

type Basis = class end

Inheritance

Object    Basis

In a finite vector space having dimension , a collection of linearly independent vectors is a basis of that space. Each basis can be represented by a matrix whose columns are given by the vectors in the basis:



The identity matrix represents the standard basis of the vector space, a kind of basis which can be instantiated by calling the static method Standard. Or, given a matrix representation , the corresponding Basis can be instantiated by calling its constructor. The matrix representation of an instance is returned by method GetBasisMatrix.

Vectors and coordinates

Each vector can be represented by its coordinates with respect to the Basis. You can evaluate the coordinates of a given set of vectors by calling GetCoordinates, or determine the vectors corresponding to given coordinates by calling GetVectors.

If both the coordinates of a vector and the corresponding basis representation are known, then the vector coordinates with respect to a new basis can be computed by calling the static method ChangeCoordinates.

Scalar products, norms, distances

Reference

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