Calculation of the Square Matrix Determinant: Computational Aspects and Alternative Algorithms

摘要

The calculation of a square matrix determinant is a typical matrix algebra operation which, if applied to big matrixes, asks for complex calculations. There are different algorithms for the determinant calculation, each one with different features under the aesthetic, functional and efficiency point of view. Besides two traditional methods such as 1. the algorithmic definition, 2. the first Laplace's theorem, during this work will be shown another method based on the primitive function (1) provided by the APL environment - that performs the calculation of a non singular square matrix inverse. Peculiar feature of some of the used algorithms is to be structurally recursive, but it is already possible to use the APL reduction operator - that plays as a valid algorithmic alternative - without the traditional lacks in the memory management that normally characterize the recursive procedures.