# Package org.apache.commons.math.linear

Linear algebra support.

See: Description

- Interface Summary
  Interface | Description
  --- | ---
  AnyMatrix | Interface defining very basic matrix operations.
  BigMatrix | Deprecated as of 2.0, replaced by `FieldMatrix` with a `BigReal` parameter
  CholeskyDecomposition | An interface to classes that implement an algorithm to calculate the Cholesky decomposition of a real symmetric positive-definite matrix.
  DecompositionSolver | Interface handling decomposition algorithms that can solve A × X = B.
  EigenDecomposition | An interface to classes that implement an algorithm to calculate the eigen decomposition of a real matrix.
  FieldDecompositionSolver<T extends FieldElement<T>> | Interface handling decomposition algorithms that can solve A × X = B.
  FieldLUDecomposition<T extends FieldElement<T>> | An interface to classes that implement an algorithm to calculate the LU-decomposition of a real matrix.
  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.
  LUDecomposition | An interface to classes that implement an algorithm to calculate the LU-decomposition of a real matrix.
  QRDecomposition | An interface to classes that implement an algorithm to calculate the QR-decomposition of a real matrix.
  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.
  RealVector | Interface defining a real-valued vector with basic algebraic operations.
  SingularValueDecomposition | An interface to classes that implement an algorithm to calculate the Singular Value Decomposition of a real matrix.
  SparseRealMatrix | Marker interface for `RealMatrix` implementations that require sparse backing storage
  SparseRealVector | Marker interface for RealVectors 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.
  AbstractRealVector | This class provides default basic implementations for many methods in the `RealVector` interface.
  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 and LU decomposition to support linear system solution and inverse.
  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.
  BigMatrixImpl | Deprecated as of 2.0, replaced by `Array2DRowFieldMatrix` with a `BigReal` parameter
  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.
  CholeskyDecompositionImpl | Calculates the Cholesky decomposition of a matrix.
  CholeskyDecompositionImpl.Solver | Specialized solver.
  DefaultFieldMatrixChangingVisitor<T extends FieldElement<T>> | Default implementation of the `FieldMatrixChangingVisitor` interface.
  DefaultFieldMatrixPreservingVisitor<T extends FieldElement<T>> | Default implementation of the `FieldMatrixPreservingVisitor` interface.
  DefaultRealMatrixChangingVisitor | Default implementation of the `RealMatrixChangingVisitor` interface.
  DefaultRealMatrixPreservingVisitor | Default implementation of the `RealMatrixPreservingVisitor` interface.
  EigenDecompositionImpl | Calculates the eigen decomposition of a real symmetric matrix.
  EigenDecompositionImpl.Solver | Specialized solver.
  FieldLUDecompositionImpl<T extends FieldElement<T>> | Calculates the LUP-decomposition of a square matrix.
  FieldLUDecompositionImpl.Solver<T extends FieldElement<T>> | Specialized solver.
  LUDecompositionImpl | Calculates the LUP-decomposition of a square matrix.
  LUDecompositionImpl.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 | Sparse matrix implementation based on an open addressed map.
  OpenMapRealVector | This class implements the `RealVector` interface with a `OpenIntToDoubleHashMap` backing store.
  QRDecompositionImpl | Calculates the QR-decomposition of a matrix.
  QRDecompositionImpl.Solver | Specialized solver.
  RealMatrixImpl | Deprecated as of 2.0 replaced by `Array2DRowRealMatrix`
  RealVector.Entry | Class representing a modifiable entry in the vector.
  RealVectorFormat | Formats a vector in components list format "{v0; v1; ...; vk-1}".
  SingularValueDecompositionImpl | Calculates the compact Singular Value Decomposition of a matrix.
  SingularValueDecompositionImpl.Solver | Specialized solver.
  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.
  TriDiagonalTransformer | Class transforming a symmetrical matrix to tridiagonal shape.

- Exception Summary
  Exception | Description
  --- | ---
  InvalidMatrixException | Thrown when a system attempts an operation on a matrix, and that matrix does not satisfy the preconditions for the aforementioned operation.
  MatrixIndexException | Thrown when an operation addresses a matrix coordinate (row, col) which is outside of the dimensions of a matrix.
  MatrixVisitorException | Thrown when a visitor encounters an error while processing a matrix entry.
  NonSquareMatrixException | Thrown when an operation defined only for square matrices is applied to non-square ones.
  NotPositiveDefiniteMatrixException | This class represents exceptions thrown when a matrix expected to be positive definite is not.
  NotSymmetricMatrixException | This class represents exceptions thrown when a matrix expected to be symmetric is not
  SingularMatrixException | Thrown when a matrix is singular.

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

Linear algebra support.

Copyright (c) 2003-2013 Apache Software Foundation