# Package org.apache.commons.math3.linear

Linear algebra support.

See: Description

Interface Summary
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.
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 | Deprecated As of version 3.1, this class is deprecated, for reasons exposed in this JIRA ticket.

Class Summary
Class | Description
--- | ---
AbstractFieldMatrix<T extends FieldElement<T>> | Basic implementation of `FieldMatrix` methods regardless of the underlying storage.
AbstractRealMatrix | Basic implementation of RealMatrix methods regardless of the underlying storage.
Array2DRowFieldMatrix<T extends FieldElement<T>> | Implementation of FieldMatrix<T> using a `FieldElement`[][] array to store entries.
Array2DRowRealMatrix | Implementation of `RealMatrix` using a `double[][]` array to store entries.
ArrayFieldVector<T extends FieldElement<T>> | This class implements the `FieldVector` interface with a `FieldElement` array.
ArrayRealVector | This class implements the `RealVector` interface with a double array.
BiDiagonalTransformer | Class transforming any matrix to bi-diagonal shape.
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.
CholeskyDecomposition.Solver | Specialized solver.
ConjugateGradient | This is an implementation of the conjugate gradient method for `RealLinearOperator`.
DefaultFieldMatrixChangingVisitor<T extends FieldElement<T>> | Default implementation of the `FieldMatrixChangingVisitor` interface.
DefaultFieldMatrixPreservingVisitor<T extends FieldElement<T>> | Default implementation of the `FieldMatrixPreservingVisitor` interface.
DefaultIterativeLinearSolverEvent | A default concrete implementation of the abstract class `IterativeLinearSolverEvent`.
DefaultRealMatrixChangingVisitor | Default implementation of the `RealMatrixChangingVisitor` interface.
DefaultRealMatrixPreservingVisitor | Default implementation of the `RealMatrixPreservingVisitor` interface.
EigenDecomposition | Calculates the eigen decomposition of a real matrix.
EigenDecomposition.Solver | Specialized solver.
FieldLUDecomposition<T extends FieldElement<T>> | Calculates the LUP-decomposition of a square matrix.
FieldLUDecomposition.Solver<T extends FieldElement<T>> | Specialized solver.
HessenbergTransformer | Class transforming a general real matrix to Hessenberg form.
IterativeLinearSolver | This abstract class defines an iterative solver for the linear system A · x = b.
IterativeLinearSolverEvent | This is the base class for all events occuring during the iterations of a `IterativeLinearSolver`.
JacobiPreconditioner | This class implements the standard Jacobi (diagonal) preconditioner.
LUDecomposition | Calculates the LUP-decomposition of a square matrix.
LUDecomposition.Solver | Specialized solver.
MatrixUtils | A collection of static methods that operate on or return matrices.
MatrixUtils.BigFractionMatrixConverter | Converter for `FieldMatrix`/`BigFraction`.
MatrixUtils.FractionMatrixConverter | Converter for `FieldMatrix`/`Fraction`.
OpenMapRealMatrix | Deprecated As of version 3.1, this class is deprecated, for reasons exposed in this JIRA ticket.
OpenMapRealVector | Deprecated As of version 3.1, this class is deprecated, for reasons exposed in this JIRA ticket.
PreconditionedIterativeLinearSolver | This abstract class defines preconditioned iterative solvers.
QRDecomposition | Calculates the QR-decomposition of a matrix.
QRDecomposition.Solver | Specialized solver.
RealLinearOperator | This class defines a linear operator operating on real (`double`) vector spaces.
RealMatrixFormat | Formats a `nxm` matrix 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.
SchurTransformer | Class transforming a general real matrix to Schur form.
SchurTransformer.ShiftInfo | Internal data structure holding the current shift information.
SingularValueDecomposition | Calculates the compact Singular Value Decomposition of a matrix.
SingularValueDecomposition.Solver | Specialized solver.
SparseFieldMatrix<T extends FieldElement<T>> | Deprecated As of version 3.1, this class is deprecated, for reasons exposed in this JIRA ticket.
SparseFieldVector<T extends FieldElement<T>> | Deprecated As of version 3.1, this class is deprecated, for reasons exposed in this JIRA ticket.
SparseRealVector | Deprecated As of version 3.1, this class is deprecated, for reasons exposed in this JIRA ticket.
SymmLQ | Implementation of the SYMMLQ iterative linear solver proposed by Paige and Saunders (1975).
SymmLQ.State | A simple container holding the non-final variables used in the iterations.
TriDiagonalTransformer | Class transforming a symmetrical matrix to tridiagonal shape.

Exception Summary
Exception | Description
--- | ---
IllConditionedOperatorException | An exception to be thrown when the condition number of a `RealLinearOperator` is 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 `RealLinearOperator` is expected.
NonSelfAdjointOperatorException | Exception to be thrown when a self-adjoint `RealLinearOperator` is 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.

## Package org.apache.commons.math3.linear Description

Linear algebra support.