Matrix operations

Matrix operations in Polylib can be found in three source files:

• matrix.c
• Matop.c
• NormalForms.c

Polylib provides function to:

• allocate, deallocate, and print matrices,
• verify if a matrix is in a specific form like the identity matrix, Hermite Normal form, or has integral components,
• add, remove columns and rows in order to perform basic modifications of matrices,
• transpose and invert matrices.

One of the most important matrix forms which is used extensively in Polylib is Hermite Normal Form (HNF).

The theoretical definition of HNF is as follows. A matrix of full row rank is said to be in Hermite normal form if it has the form:

$$A=[ \begin{array}{cc} B & 0 \end{array}]$$

where $B$ is a nonsingular, lower triangular, nonnegative matrix, in which each row has a unique maximum entry, which is located on the main diagonal of $B$.