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Matrix data structures, linear solvers, least squares methods, eigenvalue, and singular value decompositions. For larger random dense matrices (above ~ 350 x 350) matrix-matrix multiplication C = A.B is about 50% faster than MTJ.

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		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.