| Interface | Description | 
|---|---|
| AnyMatrix | Interface defining very basic matrix operations. | 
| DecompositionSolver | Interface handling decomposition algorithms that can solve A × X = B. | 
| FieldDecompositionSolver<T extends FieldElement<T>> | Interface handling decomposition algorithms that can solve A × X = B. | 
| FieldMatrix<T extends FieldElement<T>> | Interface defining field-valued matrix with basic algebraic operations. | 
| FieldMatrixChangingVisitor<T extends FieldElement<?>> | Interface defining a visitor for matrix entries. | 
| FieldMatrixPreservingVisitor<T extends FieldElement<?>> | Interface defining a visitor for matrix entries. | 
| FieldVector<T extends FieldElement<T>> | Interface defining a field-valued vector with basic algebraic operations. | 
| FieldVectorChangingVisitor<T extends FieldElement<?>> | This interface defines a visitor for the entries of a vector. | 
| FieldVectorPreservingVisitor<T extends FieldElement<?>> | This interface defines a visitor for the entries of a vector. | 
| RealMatrix | Interface defining a real-valued matrix with basic algebraic operations. | 
| RealMatrixChangingVisitor | Interface defining a visitor for matrix entries. | 
| RealMatrixPreservingVisitor | Interface defining a visitor for matrix entries. | 
| RealVectorChangingVisitor | This interface defines a visitor for the entries of a vector. | 
| RealVectorPreservingVisitor | This interface defines a visitor for the entries of a vector. | 
| SparseRealMatrix | Marker interface for  RealMatriximplementations that require sparse backing storage | 
| Class | Description | 
|---|---|
| AbstractFieldMatrix<T extends FieldElement<T>> | Basic implementation of  FieldMatrixmethods regardless of the underlying storage. | 
| AbstractRealMatrix | Basic implementation of RealMatrix methods regardless of the underlying storage. | 
| Array2DRowFieldMatrix<T extends FieldElement<T>> | Implementation of FieldMatrix FieldElement[][] array to store entries. | 
| Array2DRowRealMatrix | Implementation of  RealMatrixusing adouble[][]array to
 store entries. | 
| ArrayFieldVector<T extends FieldElement<T>> | This class implements the  FieldVectorinterface with aFieldElementarray. | 
| ArrayRealVector | This class implements the  RealVectorinterface with a double array. | 
| BlockFieldMatrix<T extends FieldElement<T>> | Cache-friendly implementation of FieldMatrix using a flat arrays to store
 square blocks of the matrix. | 
| BlockRealMatrix | Cache-friendly implementation of RealMatrix using a flat arrays to store
 square blocks of the matrix. | 
| CholeskyDecomposition | Calculates the Cholesky decomposition of a matrix. | 
| ConjugateGradient | 
 This is an implementation of the conjugate gradient method for
  RealLinearOperator. | 
| DefaultFieldMatrixChangingVisitor<T extends FieldElement<T>> | Default implementation of the  FieldMatrixChangingVisitorinterface. | 
| DefaultFieldMatrixPreservingVisitor<T extends FieldElement<T>> | Default implementation of the  FieldMatrixPreservingVisitorinterface. | 
| DefaultIterativeLinearSolverEvent | A default concrete implementation of the abstract class
  IterativeLinearSolverEvent. | 
| DefaultRealMatrixChangingVisitor | Default implementation of the  RealMatrixChangingVisitorinterface. | 
| DefaultRealMatrixPreservingVisitor | Default implementation of the  RealMatrixPreservingVisitorinterface. | 
| DiagonalMatrix | Implementation of a diagonal matrix. | 
| EigenDecomposition | Calculates the eigen decomposition of a real matrix. | 
| FieldLUDecomposition<T extends FieldElement<T>> | Calculates the LUP-decomposition of a square matrix. | 
| IterativeLinearSolver | This abstract class defines an iterative solver for the linear system A
 · x = b. | 
| IterativeLinearSolverEvent | This is the base class for all events occurring during the iterations of a
  IterativeLinearSolver. | 
| JacobiPreconditioner | This class implements the standard Jacobi (diagonal) preconditioner. | 
| LUDecomposition | Calculates the LUP-decomposition of a square matrix. | 
| MatrixUtils | A collection of static methods that operate on or return matrices. | 
| OpenMapRealMatrix | Sparse matrix implementation based on an open addressed map. | 
| OpenMapRealVector | This class implements the  RealVectorinterface with aOpenIntToDoubleHashMapbacking store. | 
| PreconditionedIterativeLinearSolver | 
 This abstract class defines preconditioned iterative solvers. | 
| QRDecomposition | Calculates the QR-decomposition of a matrix. | 
| RealLinearOperator | This class defines a linear operator operating on real ( double)
 vector spaces. | 
| RealMatrixFormat | Formats a  nxmmatrix in components list format
 "{{a00,a01, ...,
 a0m-1},{a10,
 a11, ..., a1m-1},{...},{
 an-10, an-11, ...,
 an-1m-1}}". | 
| RealVector | Class defining a real-valued vector with basic algebraic operations. | 
| RealVectorFormat | Formats a vector in components list format "{v0; v1; ...; vk-1}". | 
| RectangularCholeskyDecomposition | Calculates the rectangular Cholesky decomposition of a matrix. | 
| RRQRDecomposition | Calculates the rank-revealing QR-decomposition of a matrix, with column pivoting. | 
| SingularValueDecomposition | Calculates the compact Singular Value Decomposition of a matrix. | 
| SparseFieldMatrix<T extends FieldElement<T>> | Sparse matrix implementation based on an open addressed map. | 
| SparseFieldVector<T extends FieldElement<T>> | This class implements the  FieldVectorinterface with aOpenIntToFieldHashMapbacking store. | 
| SparseRealVector | Marker class for RealVectors that require sparse backing storage | 
| SymmLQ | 
 Implementation of the SYMMLQ iterative linear solver proposed by Paige and Saunders (1975). | 
| Exception | Description | 
|---|---|
| IllConditionedOperatorException | An exception to be thrown when the condition number of a
  RealLinearOperatoris too high. | 
| MatrixDimensionMismatchException | Exception to be thrown when either the number of rows or the number of
 columns of a matrix do not match the expected values. | 
| NonPositiveDefiniteMatrixException | Exception to be thrown when a positive definite matrix is expected. | 
| NonPositiveDefiniteOperatorException | Exception to be thrown when a symmetric, definite positive
  RealLinearOperatoris expected. | 
| NonSelfAdjointOperatorException | Exception to be thrown when a self-adjoint  RealLinearOperatoris expected. | 
| NonSquareMatrixException | Exception to be thrown when a square matrix is expected. | 
| NonSquareOperatorException | Exception to be thrown when a square linear operator is expected. | 
| NonSymmetricMatrixException | Exception to be thrown when a symmetric matrix is expected. | 
| SingularMatrixException | Exception to be thrown when a non-singular matrix is expected. | 
| SingularOperatorException | Exception to be thrown when trying to invert a singular operator. | 
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