Properties of eigenvalue function

Subject Areas : Statistics

H. Alizadeh Nazarkandi ¹ ( Departement of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran. )

Received: 2016-11-04 Accepted : 2016-12-20 Published : 2016-12-27

Keywords: پیوستگی اکید, دیفرانسیل پذیری سویی, دیفرانسیل ‌پذیری فرشه, بطور دیفرانسیل پذیر پیوسته, تجزیه طیفی, تابع مقدار ویژه,

Abstract :

For the eigenvalue function on symmetric matrices, we have gathered a number of it’s properties.We show that this map has the properties of continuity, strict continuity, directional differentiability, Frechet differentiability, continuous differentiability. Eigenvalue function will be extended to a larger set of matrices and then the listed properties will prove again.