Matrices and Linear Systems

This book presents a resume of the Matrix Calculus and the methods of Resolutionof linear System with m equations and in n unknowns assuming values in R.

This work follows after the courses of Linear Algebra that the Professor Lus Vieira, has given on the Department of Mathematics of University of University of Aveiro and on the section of Mathematics of Department of Cívil Engineering of the Faculty Engineering of University of Porto.

This book is finished with a chapter where some exercises on Matrix Calculus and Linear Systems are proposed followed with a chapter of solutions.

Components of the Book:

FRONT MATTER

Preface

Chapter 1. Matrix Calculus

1.1. Introduction
1.2. Some Notation and Some Special Matrices
1.3. Addition and Scalar Multiplication of Matrices
1.4. Multiplication of Matrices
1.5. Transposition and Conjugation of Matrices
1.6. Some Types of Complexes Matrices
1.7. Invertible Matrices
1.8. Elementary Matrices
1.9. Inverse of a Regular Matrix Recurring to Elementary Matrices
1.10. Multiplication of Matrices by Blocks
1.11. Powers of Matrices
1.12. Proposed Exercises

Chapter 2. Linear Systems

2.1. Some Concepts about Linear Systems
2.2. Classification of a Linear System
2.3. Resolution of a Linear System by the Method of Gauss-Jordan
2.4. Discussion of a Linear System with Parameters
2.5. Characteristic of a Matrix and Discussion of a Linear System
2.6. Proposed Exercises

Chapter 3. Solutions of Proposed Exercises

3.1. Solutions of Exercises of Chapter 1
3.2. Solutions of Exercises of Chapter 2

BACK MATTER

References

Readership: People who are interested in Matrix Calculus and Linear Systems.

1		FRONT MATTER PDF (6421 KB)

9		Chapter 1. Matrix Calculus PDF (425 KB)

37		Chapter 2. Linear Systems PDF (479 KB)

71		Chapter 3. Solutions of Proposed Exercises PDF (222 KB)

78		BACK MATTER PDF (1326 KB)