Condition Numbers Of Some Special Matrices

Condition number is a very important concept in the matrix theory. In this paper, we introduce the definition of the matrix norm and its basic properties. And further more we get the concept of condition number and its basic properties. Secondly, we give the estimations both of spectral and Frobenius norm condition number of a simple special triangel matrix. The two diagonal triangle matrix condition number is also studied. Finally, by the natures of the matrix norm, we will study the special Toeplitz matrix condition number and the positive definite matrix condition number. At the same time, in this paper we will give some simple numerical examples. These numerical examples can be used to verify the relevant conclusions’ reliability. This paper is mainly composed of seven chapters:In the first chapter, we introduce the background knowledge about the theory system, including its development history.In the second chapter, we introduce the definition of the matrix norm and its basic properties. We get several good properties about condition number.In the third chapter, we give the estimations both of spectral and Frobenius norm condition number of a simple matrix. At the same time, in the end of this chapter we give two simple numerical examples.In the fourth chapter, by the natures of the matrix norm, we will study the two diagonal triangle matrix condition number.In the fifth chapter, we will study the special Toeplitz matrix condition number. At the same time, we will give two simple numerical examples to verify the relevant conclusions’ reliability..In the sixth chapter, we will study the positive definite matrix condition number.In the seventh chapter, we make a summary about this paper and make a prospect about its further research.