Basic Linear Algebra. Springer Undergraduate Mathematics Series (SUMS)

Seitenzahl:

232

Gewicht:

408 g

Auflage:

, Uncorr. 3rd P.

Erschienen bei:

Springer Verlag GmbH

Kurzbeschreibung

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 of particular 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. TOC:Preface.- Forward.- The Algebra of Matrices.- Some Applications of Matrices.- Systems of Linear Equations.- Invertible Matrices.- Vector Spaces.- Linear Mappings.- The Matrix Connection.- Determinants.- Eigenvalues and Eigenvectors.- The Minimum Polynomial.- Computer Assistance.- Solutions to the Exercises.- Index.

Beschreibung

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 of particular 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.

Inhaltsverzeichnis

From of the contents:§- The Algebra of Matrices§- Some Applications of Matrices§- Systems of Linear Equations§- Invertible Matrices§- Vector Spaces§- Linear Mappings§- The Matrix Connection§- Determinants§- Eigenvalues and Eigenvectors§- The Minimal Polynomial§- Solutions to the Exercises From the contents:§- Preface§- Forward§- The Algebra of Matrices§- Some Applications of Matrices§- Systems of Linear Equations§- Invertible Matrices§- Vector Spaces§- Linear Mappings§- The Matrix Connection§- Determinants§- Eigenvalues and Eigenvectors§- The Minimum Polynomial§- Computer Assistance§- Solutions to the Exercises§- Index

Mehr über...

Mehr über:  Mathematics, Algebra, Lineare Algebra, Non-linear algebra, Mathematics / Algebra / Linear

Mehr von: 

Mehr von:  E. F. Robertson, Tom S. Blyth, John F. Montague, Springer Verlag GmbH