# 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<T> 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.