# 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.
  SparseRealMatrix | Marker interface for `RealMatrix` implementations that require sparse backing storage

- 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 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.
  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 `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 symmetric 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 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.
  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 `RealVector` interface with a `OpenIntToDoubleHashMap` backing 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.
  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.
  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 `FieldVector` interface with a `OpenIntToFieldHashMap` backing 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 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.

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