Dense and structured sparse matrices, along with matrix factorisations and solvers. The main components are:

- Matrix and vector interfaces
  - Matrix - Linear algebra matrix.
  - Vector - Linear algebra vector.
- Matrix and vector implementations
  - DenseVector - Stores the vector in a dense array.
- Dense matrices - Stores the data columnwise in a linear array.
  - DenseMatrix - Recommended matrix for general cases.
  - {Lower,Upper}{Symm,SPD}DenseMatrix - Assumes implicit symmetry, and that the matrix is positive definite (SPD). Stores entries in either the upper or lower triangular part.
  - [Unit]{Lower,Upper}TriangDenseMatrix - Only stores in the lower or upper triangular part, and assumes the rest is zero. If the matrix is unit, the main diagonal is implicitly assumes to be one.
- Packed matrices - Stores either the lower or upper triangular part of the matrix.
  - {Lower,Upper}{Symm,SPD}PackMatrix - Like their dense counterparts, but consumes less memory.
  - [Unit]{Lower,Upper}TriangPackMatrix - Also like their dense counterparts, but consumes less memory.
- Banded matrices - Stores the matrix in a dense band.
  - BandMatrix - General band matrix with the possibility of different upper and lower triangular bandwidths.
  - {Lower,Upper}{Symm,SPD}BandMatrix - Like their dense counterparts, but consumes less memory by only storing the lower or upper parts.
  - [Unit]{Lower,Upper}TriangBandMatrix - Also like their dense counterparts, but consumes less memory by only storing the lower or upper parts..
- Tridiagonal matrices - Stores just three diagonals.
  - TridiagMatrix - Standard tridiagonal matrix.
  - {Symm,SPD}TridiagMatrix - Stores only the main diagonal and an off-diagonal. May also assume that the matrix is positive definite.

- Abstract implementations
  - AbstractMatrix - Implements all the matrix operations, but doesn't specify the matrix storage.
  - AbstractVector - Implements all the vector operations, but doesn't specify the vector storage.
- Utility methods and iterators
  - Matrices - Creates submatrices and synchronized matrices. Also has several miscellaneous utility methods.
  - MatrixEntry - Entry returned when iterating over a matrix using the for-each statement.
  - VectorEntry - Entry returned when iterating over a vector using the for-each statement.
- LU decompositions
  - BandLU - LU decomposition of a banded matrix.
  - DenseLU - LU decomposition of a dense matrix.
  - BandCholesky - Cholesky decomposition of a banded matrix.
  - DenseCholesky - Cholesky decomposition of a dense SPD matrix.
  - PackCholesky - Cholesky decomposition of a packed SPD matrix.
- Orthogonal decompositions
  - LQ - LQ decomposition.
  - QL - QL decomposition.
  - QR - QR decomposition.
  - RQ - RQ decomposition.
  - GivensRotation - Givens plane rotation.
- Spectral decompositions
  - EVD - Eigenvalue decomposition of general matrices.
  - SVD - Singular value decomposition
  - SymmBandEVD - Eigenvalue decomposition of symmetrical, banded matrices.
  - SymmDenseEVD - Eigenvalue decomposition of symmetrical, dense matrices.
  - SymmPackEVD - Eigenvalue decomposition of symmetrical, packed matrices.
  - SymmTridiagEVD - Eigenvalue decomposition of symmetrical, tridiagonal matrices.