Assembly: Meta.Numerics (in Meta.Numerics.dll) Version: 2.1.0.0 (2.1.0.0)
Syntax
| C# | Visual Basic | Visual C++ | F# |
public sealed class SingularValueDecomposition
Public NotInheritable Class SingularValueDecomposition
public ref class SingularValueDecomposition sealed
[<SealedAttribute>] type SingularValueDecomposition = class end
Members
| All Members | Properties  | Methods  |
 Public Protected | Instance Static  | Declared Inherited | XNA Framework Only  .NET Compact Framework Only  |
| Member | Description | |
|---|---|---|
| ColumnCount |
Gets the number of columns in the original matrix.
|
| Dimension |
Gets the number of singular values.
|
| Equals(Object) | (Inherited from Object.) |
 | Finalize()()()() | Allows an Object to attempt to free resources and perform other cleanup operations before the Object is reclaimed by garbage collection. (Inherited from Object.) |
| GetHashCode()()()() | Serves as a hash function for a particular type. (Inherited from Object.) |
| GetType()()()() | Gets the Type of the current instance. (Inherited from Object.) |
| LeftSingularVector(Int32) |
Returns the specified left singular vector.
|
| LeftTransformMatrix()()()() |
Returns the left transform matrix.
|
| MemberwiseClone()()()() | Creates a shallow copy of the current Object. (Inherited from Object.) |
| RightSingularVector(Int32) |
Returns the specified right singular vector.
|
| RightTransformMatrix()()()() |
Returns the right transform matrix.
|
| RowCount |
Gets the number of rows in the original matrix.
|
| SingularValue(Int32) |
Gets the specificed singular value.
|
| ToString()()()() | (Inherited from Object.) |
Remarks
The singular value decomposition of a matrix represents it as a product of a left orthogonal matrix, a diagonal matrix, and a right orthogonal matrix:
The elements of the diagonal matrix are called the singular values of the original matrix.
If the orginal matrix is viewed as a linear transform operator, the rows of the right orthogonal matrix matrix form an orthonormal basis for the domain of the operator, while the columns of the left orthogonal matrix form an orthonormal basis for the range of the operator. These rows and columns are called, respectively, the right and left singular vectors of the matrix.
The right singular vectors corresponding to zero singular values span the nullspace of the matrix, that is the set of all x for which Ax = 0.
The SVD can be used to approximate the action of a high-dimensional matrix by a lower-rank one.
Use the SingularValueDecomposition()()()() of the RectangularMatrix class to obtain the SVD of an rectangular matrix, or the corresponding SingularValueDecomposition()()()() method of the SquareMatrix class to obtain the SVD of a square matrix.
