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Title Details:
Elements of Linear Algebra
Authors: Charalambous, Hara
Vavatsoulas, Charilaos
Subject: MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY > BASIC LINEAR ALGEBRA
MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY > SPECIAL MATRICES
MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY
Keywords:
Complex number
Matrix
Invertible Matrix
Gaussian Elimination Algorithm
Row Reduce Echelon Form
Rank of a Matrix
Determinant
Linear System
Homogeneus Linear System
Nullspace of a Matrix
Vector Space
Linear Dependence
Linear Independence
Vector
Linear Map
Eigenvector
Eigenvalue
Diagonalizable Matrix
Description:
Abstract:
The textbook at first covers material on complex numbers, with an emphasis on their geometric representation, their properties, the roots of unity and the Fundamental Theorem of Algebra. Then, the algebra of matrices is covered, with a discussion of Gauss' elimination method and its applications. A separate chapter is devoted to the study of the determinants of square matrices, followed by a study of the solutions of linear systems. The vector space Rn is studied, in particular R2 and R3. The definitions of lines and planes in Rn are carefully given. The solutions of linear systems are interpreted in R2 and R3 always giving an emphasis to the geometric interpretation. A chapter discussing linear functions follows and finally a chapter on eigenvectors, eigenvalues and matrix diagonalization. The textbook incorporates the use of Mathematica in a separate section in each chapter. In addition, each chapter includes a separate section with a wealth of solved exercises, while extensive hints for the exercises are given in the Appendix. Each chapter has its own bibliography. An index of terms and symbols is included.
Linguistic Editors: Kalliaras, Dimitrios
Technical Editors: Vavatsoulas, Charilaos
Type: Undergraduate textbook
Creation Date: 12-07-2023
Item Details:
ISBN 978-618-228-053-9
License: Attribution - NonCommercial - ShareAlike 4.0 International (CC BY-NC-SA 4.0)
DOI http://dx.doi.org/10.57713/kallipos-286
Handle http://hdl.handle.net/11419/10063
Bibliographic Reference: Charalambous, H., & Vavatsoulas, C. (2023). Elements of Linear Algebra [Undergraduate textbook]. Kallipos, Open Academic Editions. https://dx.doi.org/10.57713/kallipos-286
Language: Greek
Consists of:
1. Introduction to Mathematica
2. Complex Numbers, Part I
3. Complex Numbers, Part II
4. Matrices
5. Gaussian Elimination Method
6. Determinant
7. Linear Systems
8. Vectors
9. Linear Maps
10. Diagonalization
Number of pages 368
Publication Origin: Kallipos, Open Academic Editions
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