Matrices, and the rules to calculate with them, are a fundamental mathematical technique, which is often used in image processing. As such, a decent way to work with matrices had to be included within nGI.

Instead of starting from scratch, the matrix functions in NGI were influenced heavily by JAMA, the Java Matrix Package. JAMA itself was based on EISPACK, LAPACK, LINPACK and others, and uses the same algorithms as those.

The matrix support in nGI is comprised of six classes: matrix, lu_decomposition, qr_decomposition, cholesky_composition, singular_value_decomposition and eigenvalue_decomposition.

The matrix class provides the fundamental operations of numerical linear algebra. Various constructors create matrices of floating point numbers. Various gets and sets provide access to submatrices and matrix elements. The basic arithmetic operations include matrix addition and multiplication, matrix norms and selected element-by-element array operations.

Five fundamental matrix decompositions, which consist of pairs or triples of matrices, permutation vectors, and the like, produce results in five decomposition classes. These decompositions are accessed by the matrix class to compute solutions of simultaneous linear equations, determinants, inverses and other matrix functions.

The five decompositions are:

·         LU decomposition (Gaussian elimination) of rectangular matrices.

·         QR decomposition of rectangular matrices.

·         Singular value decomposition of rectangular matrices.

·         Cholesky decomposition of symmetric, positive definite matrices.

·         Eigenvalue decomposition of both symmetric and nonsymmetrical square matrices.