Topics in Matrix Analysis

  title={Topics in Matrix Analysis},
  author={Roger A. Horn and Charles R. Johnson},
1. The field of values 2. Stable matrices and inertia 3. Singular value inequalities 4. Matrix equations and Kronecker products 5. Hadamard products 6. Matrices and functions. 
Numerical Radius of Products of Special Matrices
. The purpose of this note is to present upper bounds estimations for the numerical radius of a products and Hadamard products of special matrices, including sectorial and accretive-dissipative
Equivalence of a Matrix Product to the Kronecker Product
This note aims to show that the matrix product for partitioned matrices introduced in [5] is permutation equivalent to the Kronecker product. AMS classification: 15A69
Inequalities on Singular Values of Block Triangular Matrices
Using the results, the three questions of Ando on Bloomfield--Watson-type inequalities on eigenvalues are answered and the Kantorovich inequality is generalized.
Two inequalities for the minimal eigenvalue of M-matrices
  • Qin Zhong
  • Mathematics
    Journal of Physics: Conference Series
  • 2022
M-matrices are closely related to nonnegative matrices and they have extensive application background in computational mathematics and related fields. Some properties on the minimal eigenvalue of
Some rank equalities and inequalities for Kronecker products of matrices
A set of rank equalities and inequalities are established for block matrices consisting of Kronecker products. Various consequences are also given.
Products of Real Matrices with Prescribed Characteristic Polynomials
Let A be a matrix with entries in the field of real numbers. In this paper we give necessary and sufficient conditions for the existence of real matrices B and C, with prescribed characteristic
Linear Operators on Matrices: Preserving Spectrum and Displacement Structure
In this paper, linear operators on general matrices that preserve singular values and displacement rank are characterized and thoselinear operators on Hermitian matrics that preserve eigenvalues and displacement inertia are characterized.
In this short note, we extend some known determinantal inequalities of positive definite matrices to a larger class of matrices, namely, matrices whose numerical range is contained in a sector.
Inequalities for spreads of matrix sums and products.
Let A and B be complex matrices of same dimension. Given their eigen- values and singular values, we survey and further develop simple inequalities for eigenvalues and singular values of A + B, AB ,a