All decomposition classes inherit from the
abstract base class, which defines common methods for
solving systems of simultaneous linear equations and related operations.
All these methods call the
method as needed.
Unlike for matrix types, there is no performance penalty for calling
several of these methods in succession. The decomposition is only calculated once.
method is overloaded. To solve for one right-hand side,
pass this value as a
as the first argument. To solve for multiple right-hand
sides, store the vectors in the columns of a
An optional second argument specifies
whether the right-hand sides should be overwritten with the solution. By default, a new vector or matrix instance is
created of the same dimensions as the right-hand side.
method is the same, but lets you specify the array that is to hold the result.
To solve for the transpose of a matrix, use the
To compute a least squares solution for an over-determined system, use the
A matrix is singular when not all of its rows or columns are linearly independent. The IsSingular method returns a Boolean value that
indicates this condition.
The inverse matrix is returned by the
The condition number of a matrix is defined as the ratio of its largest to its smallest singular value. Because
the calculation of singular values is a very expensive operation, an estimate that is cheaper to calculate is usually
preferred. The EstimateConditionNumber method
returns such an estimate.
The condition number gives an indication of the worst case loss of precision when solving a system of simultaneous
linear equations. The condition number of a singular matrix is infinite, which is returned as
The determinant of a matrix is returned by the
GetDeterminant method. The determinant is
only defined for square matrices.