Meta.Numerics.Matrices Namespace

	Class	Description
	AnyMatrixT	Describes the form of all matrices.
	AnyRectangularMatrix	Describes the form of all real matrices.
	AnySquareMatrix	Describes the form of all real, square matrices.
	AnyVector	Implements functionality shared between row and column vectors.
	CholeskyDecomposition	Represents the Cholesky Decomposition of a symmetric, positive definite matrix.
	ColumnVector	A column vector of real numbers.
	ComplexColumnVector	Represents a column vector of complex numbers.
	ComplexEigendecomposition	Represents a collection of complex eigenvalues and eigenvectors.
	ComplexEigenpair	Represents a complex-valued eigenvector and corresponding eigenvalue.
	ComplexEigenpairCollection	Contains a collection of complex eigenvalues and eigenvectors.
	DiagonalMatrix	Represents a diagonal matrix.
	LUDecomposition	Represents the LU decomposition of a square matrix.
	QRDecomposition	Represents a QR decomposition of a matrix.
	RealEigendecomposition	Represents a collection of real eigenvalues and eigenvectors.
	RealEigenpair	Contains a real-valued eigenvector and eigenvalue.
	RealEigenpairCollection	Contains real-valued eigenvalues and eigenvectors of a matrix.
	RectangularMatrix	A rectangular matrix of real numbers.
	RowVector	A row vector of real numbers.
	SingularValueContributor	Contains the value and left and right vectors of one term in a singular value decomposition.
	SingularValueContributorCollection	Contains all the terms contributing to the singular value decomposition of a matrix.
	SingularValueDecomposition	Stores the singular value decomposition of a matrix.
	SparseSquareMatrix	Represents a sparse, square matrix.
	SquareMatrix	Represents a square matrix.
	SquareQRDecomposition	Represents the QR decomposition of a square matrix.
	SymmetricMatrix	Represents a symmetric matrix.
	TridiagonalLUDecomposition	Represents the LU decomposition of a tri-diagonal matrix.
	TridiagonalMatrix	Represents a tri-diagonal matrix.
	UnitMatrix	Represents a unit matrix.

	Enumeration	Description
	OrderBy	Describes an ordering of eigenvalues.

You can create matrices of real values using the RectangularMatrix and SquareMatrix classes, and vectors of real values using the ColumnVector and RowVector classes. Operator overloads are defined that allow you to perform allowed arithmetic operations, such as adding two vectors or matrices, or multiplying a vector by a scalar, vector, or matrix. Each type defines methods corresponding to common linear algebra operations, such as inversion (Inverse), finding eigenvalues and eigenvectors (Eigenvalues and Eigendecomposition), and decompositions (QRDecomposition and SingularValueDecomposition).

The fastest way to solve a linear system A x = b is to form the LUDecomposition of A and call Solve(IReadOnlyListDouble) with the right-hand-side b.

There are several additional matrix containers that support smaller storage requirements and faster operations for matrices with particular structures, such as DiagonalMatrix, TridiagonalMatrix, SymmetricMatrix, and SparseSquareMatrix.

Where possible, we quickly return new matrix objects that implement a new view of existing stored values, without copying or otherwise disturbing the original values. Examples include Transpose and Row(Int32). For read-only purposes, this is much faster and requires less memory that computing and storing new values. The returned matrix objects are, however, necessarily read-only. Whether an matrix object is read-only can be determined from IsReadOnly. If you want to modify a read-only matrix object, simply make a copy using the object's Copy method (e.g. Copy or Copy).