# Matrix analysis

@inproceedings{Horn2018MatrixA, title={Matrix analysis}, author={Roger A. Horn and Charles R. Johnson}, booktitle={Statistical Inference for Engineers and Data Scientists}, year={2018} }

Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and…

## 19,164 Citations

### Positive Definite Matrices

- MathematicsOperator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
- 2019

This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real…

### Spectral theory for self-adjoint quadratic eigenvalue problems - a review

- Mathematics
- 2021

Many physical problems require the spectral analysis of quadratic matrix polynomials Mλ2+Dλ+K, λ ∈ C, with n×n Hermitian matrix coefficients, M, D, K. In this largely expository paper, we present and…

### CHAPTER 2 – A REVIEW OF SOME BASIC CONCEPTS AND RESULTS FROM THEORETICAL LINEAR ALGEBRA

- Mathematics
- 2004

### The Computation of Matrix Functions in Particular, The Matrix Exponential

- Mathematics, Computer Science
- 2010

Matrix functions in general are an interesting area in matrix analysis and are used in many areas of linear algebra and arise in numerous applications in science and engineering. We consider how to…

### Conditioning of the matrix-matrix exponentiation

- Mathematics, Computer ScienceNumerical Algorithms
- 2017

A new definition of bivariate matrix function is proposed and some general results on their Fréchet derivatives are derived, which hold, not only to the matrix-matrix exponentiation but also to other known functions, such as means of two matrices, second order FrÉchet derivatives and some iteration functions arising in matrix iterative methods.

### DISTRIBUTION RESULTS FOR A SPECIAL CLASS OF MATRIX SEQUENCES: JOINING APPROXIMATION THEORY AND ASYMPTOTIC LINEAR ALGEBRA

- Mathematics
- 2022

. In a recent paper, Lubinsky proved eigenvalue distribution results for a class of Hankel matrix sequences arising in several applications, ranging from Padé approximation to orthogonal polynomials…

### Computation of matrix gamma function

- Computer Science, MathematicsBIT Numerical Mathematics
- 2019

This research article proposes a fourth technique based on the reciprocal gamma function that is shown to be competitive with the other three methods in terms of accuracy, with the advantage of being rich in matrix multiplications.