ABSTRACT
This paper deals with the following problem: Given an n by n real symmetric positive definite matrix A and a set of positive numbers https://www.w3.org/1998/Math/MathML"> { λ i } 1 n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003419839/4baaeab4-d6e3-45ed-9dec-1deb90c341dd/content/inline-math574.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , find a positive diagonal matrix D such that DAD has eigenvalues https://www.w3.org/1998/Math/MathML"> { λ i } 1 n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003419839/4baaeab4-d6e3-45ed-9dec-1deb90c341dd/content/inline-math575.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . Necessary conditions for the solvability of this problem are derived.
