MH4713 — Linear Algebra
This module is currently taught by my colleague Diarmuid O'Driscoll.
Contact Information
| Name | Dr. Bernd Kreussler |
| Office | N29 |
| Internal Telephone | 4578 |
| bernd.kreussler@mic.ul.ie | |
| WWW | www.maths.mic.ul.ie/kreussler/ |
Some Links of interest
- A First Course in Linear Algebra, a textbook by Robert Beezer, free for downloading.
- Linear algebra textbook by Jim Hefferon free for downloading.
- Mathematical discussions by Timothy Gowers (University of Cambridge)
Contents of the lecture delivered during the autumn semester 2005
- Systems of Linear Equations
- The algebra-geometry dictionary
- The method of Gauss to solve linear equations
- Vector Spaces
- Definitions and examples of vector spaces
- Basic properties of vector spaces
- Bases and coordinates
- Linear Mappings
- Definitions and examples of linear mappings
- Linear mappings and matrices
- Product of matrices
- Rank and regularity
- Applications
- Determinants
- Definition and computation of determinants
- Length and Angle
- The inner product, length and angle
- Orthonormal bases, Gram-Schmidt process
- Endomorphisms
- Eigenvectors and Eigenvalues
- Computations
Textbooks
Section 512.5 on the shelves in the library is full of useful books. Some of them are listed below.
- Jänich, Klaus: Linear algebra, (Springer-Verlag) 1994
- Sernesi, Edoardo: Linear algebra: a geometric approach, (Chapman & Hall) 1993
- Lang, Serge: Linear algebra (Springer-Verlag) 1987
- Morris, A. O.: Linear algebra: an introduction. (Van Nostrand Reinhold) 1982
- Smith, Larry: Linear algebra, (Springer-Verlag) 1978
- Bradley, Gerald L: A primer of linear algebra, (Prentice-Hall) 1974
- Lipschutz, Seymour: Schaum's outline of theory and problems of linear algebra, (McGraw-Hill) 1974
- Ayres, Frank: Schaum's outline of theory and problems of matrices (McGraw-Hill) 1974
- O'Nan, Michael: Linear algebra, (Harcourt Brace Jovanovich) 1970
