# Extreme.Mathematics.LinearAlgebra Namespace

The Extreme.LinearAlgebra namespace contains classes for working with vectors and matrices and matrix decompositions, and for solving systems of simultaneous linear equations and least squares problems.

## Classes

 BandMatrix Represents a sparse matrix with nonzero elements only on a diagonal band containing the main diagonal. BlockVector Represents a vector that is made up of smaller vectors. CholeskyDecomposition Represents the Cholesky decomposition of a positive-definite symmetric matrix. ComplexSingularValueDecomposition Represents the singular value decomposition of a matrix. ComponentReadOnlyException Represents an exception that is thrown when an attempt is made to set a component of a Vector or Matrix whose value is fixed. ComposedComplexMatrix Represents a complex matrix that is composed from real matrices that represent the real and imaginary components. ComposedComplexVector Represents a complex vector composed of a vector of real and of imaginary components. ConstantMatrix Represents a matrix whose components all have the same value.. ConstantVector Represents a vector whose elements are all the same. Decomposition Represents a matrix decomposition. DenseMatrix Represents a general, dense, square or rectangular matrix. DenseVector Represents a vector with arbitrary components. DiagonalMatrix Represents a matrix whose only nonzero components lie on a diagonal. EigenvalueDecomposition Represents the eigenvalue decomposition of a dense matrix. GeneralizedDecomposition Represents a generalized matrix decomposition. GeneralizedEigenvalueDecomposition Represents the generalized eigenvalue decomposition of two matrices. GeneralizedSingularValueDecomposition Represents the generalized singular value decomposition of two matrices. HermitianMatrix Represents a matrix that is Hermitian about the main diagonal. IndexedVector Represents a vector whose elements are arbitrary components of another vector. LeastSquaresSolver Represents the solution to a least squares problem. LinearAlgebraOperations Specifies the methods that must be implemented by a class to support basic linear algebra. LinearOperator Defines methods for the solution of a system of simultaneous linear equations and related operations. LQDecomposition Represents the LQ decomposition of a matrix. LUDecomposition Represents the LU decomposition of a matrix. MatrixNotPositiveDefiniteException Represents an exception that is thrown when a computation cannot be completed because a matrix is not positive definite. MatrixSingularException Represents an exception that is thrown when a computation cannot be completed because a matrix is singular. MatrixView Represents a view on all or part of a matrix. NonHermitianEigenvalueDecomposition Represents the eigenvalue decomposition of a complex matrix. NonNegativeMatrixFactorization Represents a non-negative decomposition of a general matrix. PermutationMatrix Represents a permutation matrix. QLDecomposition Represents the QL decomposition of a matrix. QRDecomposition Represents the QR decomposition of a matrix. RealEigenvalueDecomposition Represents the eigenvalue decomposition of a non-symmetric, real matrix. RQDecomposition Represents the RQ decomposition of a matrix. SingularValueDecomposition Represents the singular value decomposition of a matrix. SparseCompressedColumnMatrix Represents a sparse matrix in Compressed Sparse Column format. SparseMatrix Represents a sparse matrix. SparseVector Represents a vector with a vector with relatively few non-zero components. SymmetricIndefiniteDecomposition Represents the symmetric indefinite (Bunch-Kaufman) decomposition of a symmetric matrix. SymmetricMatrix Represents a matrix that is symmetrical about the main diagonal. TriangularMatrix Represents a matrix whose elements above or below the main diagonal are zero.

## Structures

 ColumnCollection Represents the collection of columns of a matrix. IndexValuePair Represents the value of a component at a specified position in a vector. PivotVector Represents a vector containing permutation indexes. RowCollection Represents the collection of rows of a matrix. RowColumnValueTriplet Represents the value of a component at a specified position in a matrix.

## Interfaces

 IResizableMatrix Represents the methods available for matrices that can be resized.

## Enumerations

 CloningMethod Enumerates the methods that can be used to clone a Vector or Matrix. EigenvalueRange Enumerates the options for specifying the eigenvalues that should be computed. GeneralizedSingularValueDecompositionFactors Enumerates the factors of a GeneralizedSingularValueDecomposition. LeastSquaresSolutionMethod Enumerates the possible methods for solving a least squares problem. SingularValueDecompositionFactors Enumerates the factors of a SingularValueDecomposition.