Inertia of the matrix

  • Rajendra Bhatia

    Indian Statistical Institute, New Delhi, India
  • Tanvi Jain

    Indian Statistical Institute, New Delhi, India

Abstract

Let be positive real numbers. It is well known that for all the matrix is positive definite. Our main theorem gives a count of the number of positive and negative eigenvalues of this matrix when : Connections with some other matrices that arise in Loewner’s theory of operator monotone functions and in the theory of spline interpolation are discussed.

Cite this article

Rajendra Bhatia, Tanvi Jain, Inertia of the matrix . J. Spectr. Theory 5 (2015), no. 1, pp. 71–87

DOI 10.4171/JST/91