New Estimations For Numerical Characteristics Bounds Of Matrices

As everyone knows, Matrix theory can be traced back in history, at least Sylvester and Cayley, in particular, Cayley's work of 1858 years. Some subjects of modern mathematics, such as the algebraic structure theory and functional analysis, would be found in the Matrix theory. As a tool, Matrix theory is applied widely in mathematics and engineering disciplines.Numerical characteristics of the matrix are: eigenvalues, singular value, determinant, norm, etc., which are a function of matrix elements of their own. During the study process, we find that the estimated value of features of matrix has an important significance in the application and has been widespread concern about the hot topics.In this paper, numerical characteristics of the matrix have been further research. The main results and innovations are as follows:1. The positive definite matrix are divided as follow Denote Then, we can get that which extends the Schur's inequality;2. We promote the Ostrowski-Taussky inequality, get a more enhanced inequality3. We present a new estimate of matrix's spread: Then we use several numerical examples verify the validity of the results;4. We present a new estimate of matrix's determinant: This is the extension of Hadamard inequality. Then we use a numerical example verifies the validity of the results.