 | Basis Class |
Inheritance HierarchyNamespace: Novacta.Analytics.Advanced
Assembly: Novacta.Analytics (in Novacta.Analytics.dll) Version: 2.0.0
SyntaxThe Basis type exposes the following members.
ConstructorsProperties
Methods| Name | Description | |
|---|---|---|
  | ChangeCoordinates |
Gets coordinates of vectors with respect to a new basis
given the coordinates
with respect to another basis.
|
| Distance |
Computes the distance between vectors having the specified coordinates.
|
| Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) |
 | Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) |
| GetBasisMatrix |
Gets the matrix representation of the Basis.
|
| GetCoordinates |
Gets the coordinates of the given vectors with respect to
the Basis.
|
| GetHashCode | Serves as the default hash function. (Inherited from Object.) |
| GetType | Gets the Type of the current instance. (Inherited from Object.) |
| GetVectors |
Gets the vectors represented by the specified coordinates
with respect to the Basis.
|
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) |
| Norm |
Returns the norm of the vector having the specified coordinates.
|
| ScalarProduct |
Return the scalar product of the vectors having the specified
coordinates.
|
| Standard |
Returns the standard basis of the specified dimension.
|
| ToString | Returns a string that represents the current object. (Inherited from Object.) |
Remarks
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
A Basis endows a vector space with a scalar product, which in turn induces the definition of a norm for a vector and that of a distance between vectors. Such quantities can be computed by calling methods ScalarProduct, Distance, and Norm, respectively. All such functions require, as arguments, the coordinates of the vectors under study.See Also