public abstract class ComplexMatrix : ComplexLinearOperator, 
	IFormattable, IStructuralEquatable

Public MustInherit Class ComplexMatrix
	Inherits ComplexLinearOperator
	Implements IFormattable, IStructuralEquatable

public ref class ComplexMatrix abstract : public ComplexLinearOperator, 
	IFormattable, IStructuralEquatable

[<AbstractClassAttribute>]
type ComplexMatrix =  
    class
        inherit ComplexLinearOperator
        interface IFormattable
        interface IStructuralEquatable
    end

The ComplexMatrix type exposes the following members.

	Name	Description
	ComplexMatrix(Int32, Int32)	Constructs a new ComplexMatrix of the specified dimensions using the specified values array.
	ComplexMatrix(SerializationInfo, StreamingContext)	Constructs a new ComplexMatrix from serialization values.

	Name	Description
	ColumnCount	Gets the number of columns in the ComplexMatrix.
	Columns	Gets the ComplexColumnCollection for this instance.
	ElementOrder	Gets a value indicating the order in which the matrix elements are stored.
	IsHermitian	Gets a value that indicates if the matrix is equal to its conjugate transpose.
	IsLowerTriangular	Gets a value that indicates if all elements of the matrix above the main diagonal are zero.
	IsSymmetrical	Gets a value that indicates if the matrix is symmetrical about the main diagonal.
	IsUnitDiagonal	Gets a value indicating whether all diagonal elements of this instance are equal to 1.
	IsUpperTriangular	Gets a value that indicates if all elements of the matrix below the main diagonal are zero.
	ItemInt32, Range	Gets or sets the components of a row of this ComplexMatrix.
	ItemInt32, Int32	Gets or sets the specified element in this ComplexMatrix.
	ItemRange, Range	Gets or sets the components of a submatrix of this ComplexMatrix.
	ItemRange, Int32	Gets or sets the components of a column of this ComplexMatrix.
	RowCount	Gets the number of rows in the ComplexMatrix.
	Rows	Gets the ComplexRowCollection for this instance.

	Name	Description
	Add(ComplexMatrix, ComplexMatrix)	Adds two ComplexMatrix objects.
	Add(TransposeOperation, TransposeOperation, DoubleComplex, ComplexMatrix)	Adds a multiple of a ComplexMatrix to this ComplexMatrix and returns the result.
	AddProductToVector	Multiplies a ComplexVector by this ComplexMatrix and stores the result in a second vector of type ComplexDenseVector.
	AsDenseMatrix	Returns this matrix as a general matrix. ComplexDenseMatrix.
	Clone	Constructs a deep copy of this ComplexMatrix.
	CloneData	Gives this instance its own copy of its elements.
	ComponentwiseDivide(ComplexMatrix)	Obsolete. Divides the components of this instance by the corresponding components of another matrix.
	ComponentwiseDivide(ComplexMatrix, ComplexMatrix)	Obsolete. Divides the components of a ComplexMatrix by the corresponding components of another matrix.
	ComponentwiseMultiply(ComplexMatrix)	Obsolete. Multiplies the components of this instance by the corresponding components of another matrix.
	ComponentwiseMultiply(ComplexMatrix, ComplexMatrix)	Obsolete. Multiplies the components of a ComplexMatrix by the corresponding components of another matrix.
	Conjugate	Returns the conjugate transpose of this instance.
	ConjugateTranspose	Returns the conjugate transpose of this instance.
	CopyTo	Copies the components of this ComplexMatrix to another matrix.
	Create(DoubleComplex)	Constructs a new matrix from a two-dimensional array.
	Create(Int32, Int32)	Constructs a new matrix with the specified number of rows and columns
	Create(Int32, Int32, DoubleComplex)	Constructs a new matrix with the specified number of rows and columns whose elements are all equal to the specified value.
	Create(Int32, Int32, DoubleComplex, MatrixElementOrder)	Constructs a new matrix of the specified dimensions using the specified values array.
	Create(Int32, Int32, DoubleComplex, MatrixElementOrder, Boolean)	Constructs a new matrix of the specified dimensions using the specified values array.
	Create(Int32, Int32, DoubleComplex, Int32, Int32, MatrixElementOrder)	Constructs a new matrix.
	CreateConstant	Constructs a new constant matrix.
	CreateDiagonal(Int32)	Constructs a new ComplexDiagonalMatrix.
	CreateDiagonal(ComplexVector)	Constructs a new ComplexDiagonalMatrix.
	CreateHermitian(Int32)	Constructs a new Hermitian matrix with the specified dimension.
	CreateHermitian(Int32, DoubleComplex, MatrixTriangle)	Constructs a new Hermitian matrix of the specified dimension using the specified values.
	CreateHermitian(Int32, DoubleComplex, MatrixTriangle, Boolean)	Constructs a new Hermitian matrix of the specified dimension using the specified values.
	CreateLowerTriangular(Int32)	Constructs a new lower triangular matrix.
	CreateLowerTriangular(Int32, Int32)	Constructs a new lower triangular matrix.
	CreateLowerTriangular(Int32, Int32, MatrixDiagonal)	Constructs a new lower triangular matrix.
	CreateLowerTriangular(Int32, Int32, DoubleComplex, MatrixElementOrder)	Constructs a new lower triangular matrix.
	CreateLowerTriangular(Int32, Int32, DoubleComplex, MatrixDiagonal, MatrixElementOrder, Boolean)	Constructs a new lower triangular matrix.
	CreateUpperTriangular(Int32)	Constructs a new upper triangular matrix.
	CreateUpperTriangular(Int32, Int32)	Constructs a new upper triangular matrix.
	CreateUpperTriangular(Int32, Int32, MatrixDiagonal)	Constructs a new upper triangular matrix.
	CreateUpperTriangular(Int32, Int32, DoubleComplex, MatrixElementOrder)	Constructs a new upper triangular matrix.
	CreateUpperTriangular(Int32, Int32, DoubleComplex, MatrixDiagonal, MatrixElementOrder, Boolean)	Constructs a new upper triangular matrix.
	ElementwiseDivide	Divides the components of a ComplexMatrix by the corresponding components of another matrix.
	ElementwiseDivideInPlace	Divides the components of this instance by the corresponding components of another matrix.
	ElementwiseMultiply	Multiplies the components of a ComplexMatrix by the corresponding components of another matrix.
	ElementwiseMultiplyInPlace	Multiplies the components of this instance by the corresponding components of another matrix.
	Equals(Object)	Determines whether the specified Object is equal to the current ComplexMatrix. (Overrides ObjectEquals(Object).)
	Equals(Object, IEqualityComparer)	Returns whether an object is structurally equal to this instance.
	EstimateConditionNumber	Calculates an estimate for the condition number of this ComplexMatrix. (Overrides ComplexLinearOperatorEstimateConditionNumber.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	FrobeniusNorm	Returns the Frobenius norm of this ComplexMatrix.
	GetCholeskyDecomposition	Returns the Cholesky decomposition of the matrix.
	GetCholeskyDecomposition(Boolean)	Returns the Cholesky decomposition of the matrix.
	GetColumn(Int32)	Returns a column complex vector for this instance that points at the specified column.
	GetColumn(Int32, Range)	Returns a column complex vector for this instance starting at the specified column and row and of the specified length.
	GetColumn(Int32, Int32, Int32)	Returns a column complex vector for this instance starting at the specified column and row and of the specified length.
	GetColumn(Int32, Int32, Int32, Int32)	Returns a column complex vector for this instance starting at the specified column and row and of the specified length.
	GetColumnEnumerator	Obsolete. Gets an IEnumerator than can be used to enumerate the columns of this ComplexMatrix.
	GetComponents	Obsolete. Gets the components of the complex vector.
	GetComponents(MatrixElementOrder)	Obsolete. Gets the components of the complex vector.
	GetConditionNumber	Calculates the condition number of this matrix.
	GetDeterminant	Calculates the determinant of this ComplexMatrix. (Overrides ComplexLinearOperatorGetDeterminant.)
	GetDiagonal	Gets a complex vector view of the diagonal elements of this instance.
	GetDiagonal(Int32)	Gets a complex vector view of the specified diagonal of this instance.
	GetEigenvalueDecomposition	Returns the eigenvalue decomposition for this matrix.
	GetEigenvalueDecomposition(Boolean)	Returns the eigenvalue decomposition for this matrix.
	GetHashCode	Returns the hash code for this instance. (Overrides ObjectGetHashCode.)
	GetHashCode(IEqualityComparer)	Returns a hash code for this instance.
	GetImaginaryPart	Returns a real matrix containing the imaginary elements of the matrix.
	GetInverse	Calculates the inverse matrix.. (Inherited from ComplexLinearOperator.)
	GetInverse(Boolean)	Calculates the inverse of this ComplexMatrix. (Overrides ComplexLinearOperatorGetInverse(Boolean).)
	GetLUDecomposition	Returns the LU decomposition of the matrix.
	GetLUDecomposition(Boolean)	Returns the LU decomposition of the matrix.
	GetObjectData	Populates a SerializationInfo with the values needed to serialize the target object. (Overrides ComplexLinearOperatorGetObjectData(SerializationInfo, StreamingContext).)
	GetQRDecomposition	Returns the QR decomposition of the matrix.
	GetQRDecomposition(Boolean)	Returns the QR decomposition of the matrix.
	GetRealPart	Returns a real matrix containing the real elements of the matrix.
	GetRow(Int32)	Returns a row complex vector for this instance that points at the specified row.
	GetRow(Int32, Range)	Returns a row complex vector for this instance starting at the specified row and column and of the specified length.
	GetRow(Int32, Int32, Int32)	Returns a row complex vector for this instance over the specified range.
	GetRow(Int32, Int32, Int32, Int32)	Returns a row complex vector for this instance starting at the specified row and column and of the specified length.
	GetRowEnumerator	Obsolete. Returns an IEnumeratorT that allows you to enumerate the rows of this ComplexMatrix.
	GetSingularValueDecomposition	Returns the singular value decomposition of the matrix.
	GetSingularValueDecomposition(SingularValueDecompositionFactors)	Returns the singular value decomposition of the matrix.
	GetSingularValueDecomposition(SingularValueDecompositionFactors, Boolean)	Returns the singular value decomposition of the matrix.
	GetSingularValues	Gets a vector containing the singular values of the matrix.
	GetSubmatrix(Range, Range)	Gets a ComplexMatrix that is a submatrix of this ComplexMatrix.
	GetSubmatrix(Range, Range, TransposeOperation)	Gets a ComplexMatrix that is a submatrix of this ComplexMatrix.
	GetSubmatrix(Int32, Int32, Int32, Int32)	Gets a ComplexMatrix that is a submatrix of this ComplexMatrix.
	GetSubmatrix(Int32, Int32, Int32, Int32, Int32, Int32, TransposeOperation)	Gets a ComplexMatrix that is a submatrix of this ComplexMatrix.
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	GetValue	Gets the matrix component at the specified position.
	InfinityNorm	Returns the infinity norm of this ComplexMatrix.
	IsComponentWritable	Obsolete. Returns whether the value of the component at the specified row and column can be changed.
	IsElementWritable	Returns whether the value of the component at the specified row and column can be changed.
	IsSingular	Gets a value indicating whether this matrix is singular. (Overrides ComplexLinearOperatorIsSingular.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	Multiply(ComplexMatrix)	Applies the matrix to a matrix. (Overrides ComplexLinearOperatorMultiply(ComplexMatrix).)
	Multiply(ComplexVector)	Applies the matrix to a vector. (Overrides ComplexLinearOperatorMultiply(ComplexVector).)
	Multiply(DoubleComplex)	Multiplies this ComplexMatrix by a scalar factor.
	Multiply(ComplexMatrix, ComplexMatrix)	Multiplies two ComplexMatrix objects.
	Multiply(ComplexMatrix, ComplexVector)	Multiplies a ComplexVector by a ComplexMatrix.
	Multiply(ComplexVector, ComplexMatrix)	Multiplies a ComplexVector by a ComplexMatrix.
	Multiply(MatrixOperationSide, TransposeOperation, TransposeOperation, ComplexMatrix)	Multiplies this ComplexMatrix by another matrix and returns the result.
	MultiplyTranspose(ComplexMatrix)	Applies the transpose of the matrix to a matrix. (Overrides ComplexLinearOperatorMultiplyTranspose(ComplexMatrix).)
	MultiplyTranspose(ComplexVector)	Applies the transpose of the matrix to a vector. (Overrides ComplexLinearOperatorMultiplyTranspose(ComplexVector).)
	OneNorm	Returns the 1-norm of this ComplexMatrix.
	PermuteColumns	Permutes the columns of the matrix using the specified Permutation.
	PermuteRows	Permutes the rows of the matrix using the specified Permutation.
	PermuteRowsAndColumns(Permutation)	Permutes the rows and columns of the matrix using the specified Permutation.
	PermuteRowsAndColumns(Permutation, Permutation)	Permutes the rows and columns of the matrix using the specified row and column Permutation.
	Rank	Returns the numerical rank of a matrix. (Inherited from ComplexLinearOperator.)
	Rank(Double)	Returns the numerical rank of a matrix using the specified tolerance. (Overrides ComplexLinearOperatorRank(Double).)
	ScaleColumns	Scales the columns of the matrix by the values specified by a vector.
	ScaleRows	Scales the rows of the matrix by the values specified by a vector.
	SetToZero	Sets all elements of the matrix to zero.
	SetValue(DoubleComplex)	Sets all elements of the matrix to the specified value.
	SetValue(DoubleComplex, Int32, Int32)	Sets the matrix component at the specified position to the specified value.
	ShallowCopy	Makes a shallow copy of this ComplexMatrix.
	Solve(ComplexMatrix)	Solves the system of linear equations for the specified right-hand side ComplexMatrix. (Inherited from ComplexLinearOperator.)
	Solve(ComplexVector)	Solves the system of linear equations for the specified right-hand side complex vector. (Inherited from ComplexLinearOperator.)
	Solve(ComplexDenseMatrix, Boolean)	Solves the system of simultaneous linear equations for the specified right-hand side ComplexDenseMatrix and overwrites the right-hand side with the solution. (Overrides ComplexLinearOperatorSolve(ComplexDenseMatrix, Boolean).)
	Solve(ComplexDenseVector, Boolean)	Solves the system of simultaneous linear equations for the specified right-hand side complex vector. (Overrides ComplexLinearOperatorSolve(ComplexDenseVector, Boolean).)
	SolveTranspose(ComplexMatrix)	Solves the transposed system of linear equations for the specified right-hand side ComplexMatrix. (Inherited from ComplexLinearOperator.)
	SolveTranspose(ComplexVector)	Solves the system of linear equations for the specified right-hand side complex vector. (Inherited from ComplexLinearOperator.)
	SolveTranspose(ComplexDenseMatrix, Boolean)	Solves the transposed system of linear equations for the specified right-hand side ComplexDenseMatrix and optionally overwrites the right-hand side with the solution. (Overrides ComplexLinearOperatorSolveTranspose(ComplexDenseMatrix, Boolean).)
	SolveTranspose(ComplexDenseVector, Boolean)	Solves the transposed system of linear equations for the specified right-hand side ComplexDenseVector and optionally overwrites the right-hand side with the solution. (Overrides ComplexLinearOperatorSolveTranspose(ComplexDenseVector, Boolean).)
	Subtract	Subtracts two ComplexMatrix objects.
	SwapColumns	Swaps the columns with the specified indices.
	SwapRows	Swaps the rows with the specified indices.
	ToArray	Gets the components of the complex vector.
	ToArray(MatrixElementOrder)	Gets the components of the complex vector.
	ToDenseMatrix	Makes a copy of this instance and returns it as a ComplexDenseMatrix.
	ToGeneralMatrix	Obsolete. Makes a copy of this instance and returns it as a ComplexDenseMatrix.
	ToString	Returns a String representation of this ComplexMatrix. (Overrides ObjectToString.)
	ToString(String)	Returns a String representation of this ComplexMatrix.
	ToString(String, IFormatProvider)	Returns a String representation of this ComplexMatrix.
	Trace	Gets the sum of the diagonal elements of this ComplexMatrix.
	Transpose	Returns the transpose of this instance.
	UnscaleColumns	Scales the columns of the matrix by the inverse of the values specified by a vector.
	UnscaleRows	Scales the rows of the matrix by the inverse of the values specified by a vector.

	Name	Description
	Addition	Adds two ComplexMatrix objects.
	Equality	Returns a value indicating whether two instances of ComplexMatrix are equal.
	Inequality	Returns a value indicating whether two instances of ComplexMatrix are not equal.
	Multiply(ComplexMatrix, ComplexMatrix)	Multiplies two ComplexMatrix objects.
	Multiply(ComplexMatrix, ComplexVector)	Multiplies a ComplexVector by a ComplexMatrix.
	Multiply(ComplexVector, ComplexMatrix)	Multiplies a ComplexVector by a ComplexMatrix.
	Subtraction	Subtracts two ComplexMatrix objects.

ComplexMatrix is the base class for representing real matrices, two-dimensional arrays of double-precision floating-point numbers. An application can perform operations on matrices using instances of the ComplexMatrix class, while descendant classes implement specialized algorithms for specific types of matrices.

The ComplexMatrix class provides methods and properties for all the common operations on matrices, including arithmetic operations, calculating norms and solving systems of simultaneous linear equations. Various methods allow you to access individual components as well as rows and columns and submatrices.

Since ComplexMatrix is an base class and cannot be instantiated directly. Instead, use one of its derived classes. These are:

Note that the specialized classes exploit certain structural properties to perform many calculations more quickly than the general algorithms implemented by ComplexMatrix.

ComplexMatrix provides an indexer property. For convenient access to the rows or columns of a ComplexMatrix or parts thereof, use the GetRow(Int32) and GetColumn(Int32) methods.

Overloaded versions of the major arithmetic operators are provided for languages that support them. For languages that don't support operator overloading, equivalent methods are supplied.

Many matrix decompositions exist, serving a variety of purposes. Each of them has its own class. In this release the LU decomposition and the QR decomposition are supported. For positive-definite hermitian matrices, the ComplexCholeskyDecomposition is available.

Numerical Libraries

Reference