On The Estimation Of Upper Bounds For Determinants Of Two Matrices

Matrix perturbation mainly studies the effect that the variances of matrix elements influence the sequence of matrix Calculation results. It is not only related with matrix theory, but also it is important to calculation estimation of determinant for matrix.The purpose of this paper is to study the additive perturbation of determinant for matrix. Some new absolute and relative perturbation bounds of determinant are obtained, which improves previous results.The details will go as follows:Firstly, the current study situation and basic knowledge of matrix perturbation analysis are introduced.Secondly, we derive absolute perturbation bound of determinant by using the properties of determinant, matrix spectrum norm and singular value decomposition.Lastly, this paper introduces a new norm. Using the advantage of the norm, and combing with the singular value decomposition of matrix, properties of determinant, we derive the absolute and relative perturbation bounds of determinant for matrix. By comparing with the existing results, the results that we obtain are better.