Linear Algebra

This is a first course in linear algebra. The course will lay down the basic concepts and techniques of linear algebra needed for subsequent study. At the same time, it will provide an appreciation of the wide application of this discipline within the scientific field.

The course will require development of theoretical results. Proofs and consequences of such results will require the use of mathematical rigour, algebraic manipulation, geometry and numerics.

A goal of the course is to provide insight into how linear algebra theorems and results, sometimes quite abstract, impinge on everyday life. This will be illustrated with detailed examples.

At the end of this course the student will be capable of gained the ability to:

• Comprehend vector spaces (subspaces).
• Understand fundamental properties of matrices including inverse matrices, eigenvalues and linear transformations. 
• Be able to solve linear systems of equations.
• Have an insight into the applicability of linear algebra.

• Vectors: Vectors and geometry in two and three space dimensions, Algebraic properties, Dot products and orthogonality, Linear independence, Basis, Dimension, Vector spaces and subspaces. [1,4]
• Matrices: Matrix operations, Column and row space, Null and range space, rank, Determinants, Inverse matrices, Population growth, Error correcting codes. [2,4]
• Linear transformations: Definition and examples, Properties, Composition, Rotations and reflections, Matrices, One-to-one and onto, Robotics [2,4]
• Solution of linear systems: Examples of linear systems, Problems arising from solving on a Computer, Row echelon form, Gaussian elimination, Pivoting, Network analysis, Global positioning system [3,4]
• Eigenvalues and eigenvectors: Definition, Similarity and diagonalization, Population growth revisited, Systems of linear differential equations [2,4]

• Vector spaces and subspaces (4 lectures)
• Matrices (4 lectures)
• Inverse matrices (3 lectures)
• Linear transformations (5 lectures)
• Solution of linear systems (5 lectures)
• Eigenvalues and eigenvectors (3 lectures)

• Introduction to linear algebra (3rd Edition), Gilbert Strang, Wellesley-Cambridge press.