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Basic Linear Algebr 2nd edition by Blyth, Robertson ISBN 1852336625 9781852336622

Name: Basic Linear Algebr 2nd edition by Blyth, Robertson ISBN 1852336625 9781852336622
SKU: EB-24964
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Authors:Thomas S. Blyth, Edmund F. Robertson , Series:Mathematics [37] , Author sort:Thomas S. Blyth, Edmund F. Robertson , Published:Published:Oct 1997 , Publisher:Springer

SKU: EB-24964 Category: eBook DJVU Tags: Algebr 2nd, Basic, Blyth, Linear, Robertson

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Basic Linear Algebr 2nd edition by T.S. Blyth, E.F. Robertson – Ebook PDF Instant Download/Delivery. 1852336625, 978-1852336622
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Product details:

ISBN 10: 1852336625
ISBN 13: 978-1852336622
Author: T.S. Blyth, E.F. Robertson

Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity. This new and revised edition features additional exercises and coverage of Cramer’s rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be ofparticular interest to readers: this will take the form of a tutorial on the use of the “LinearAlgebra” package in MAPLE 7 and will deal with all the aspects of linear algebra developed within the book.

Basic Linear Algebr 2nd Table of contents:

1. The Algebra of Matrices

Introduction to matrices and their operations
Matrix addition, multiplication, and scalar multiplication
Special types of matrices (e.g., identity, diagonal, symmetric)

2. Some Applications of Matrices

Matrices in real-world problems
Applications in computer graphics, physics, economics, etc.

3. Systems of Linear Equations

Solving systems using matrices
Row reduction and Gaussian elimination
Matrix representations of systems of linear equations

4. Invertible Matrices

Conditions for matrix invertibility
Finding the inverse of a matrix
Applications of invertible matrices

5. Vector Spaces

Definition and properties of vector spaces
Subspaces, span, and linear independence
Basis and dimension of vector spaces

6. Linear Mappings

Definition of linear maps between vector spaces
The kernel and image of a linear map
Matrix representation of linear maps

7. The Matrix Connection

Relationship between matrices and linear transformations
Change of basis and similarity of matrices
Diagonalization of matrices

8. Determinants

Definition and properties of the determinant
Calculating the determinant of a matrix
Applications of determinants in solving systems and finding inverses

9. Eigenvalues and Eigenvectors

The concept of eigenvalues and eigenvectors
Finding eigenvalues and eigenvectors
Diagonalization of matrices using eigenvalues

10. The Minimum Polynomial

Definition and importance of the minimal polynomial
Finding the minimal polynomial of a matrix
Applications of minimal polynomials in diagonalization

11. Computer Assistance

Using software tools for matrix computations
Numerical methods for eigenvalue computation
Computer-assisted solutions to linear algebra problems

12. Solutions to the Exercises

Detailed solutions to the problems and exercises presented throughout the book

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