NUMERO DE CONDICION Y DETERMINANTE DE UNA MATRIZ

Abstract

In computational resolution of linear algebraic systems Ax = b by direct methods, the condition number
of A plays an important role:
cond(A) = ||A|| ||A-1||
since the attainable precision of the computer solution is determined by it. We might think that if A is ill conditioned with respect to the used precision, its determinant det(A) is close to 0, and conversely. Sometimes tradition has considered both situations as equivalent; however this is not true, although they are relationed. In this paper, the reciprocal influence between determinant and condition number is explained and examples to disprove this statement are given