An introduction to linear algebra concluding with an introduction to abstract vector spaces.

The principal topics are vectors, systems of linear equations, matrices. The important notions of linear independence, span and bases are introduced.

This course is both a preparation for the practical use of vectors, matrices and systems of equations and also lays the groundwork for a more abstract, pure-mathematical treatment of vector spaces.

Matrix calculus

• Operations on matrices
• Determinant

Linear systems

• Gauss algorithm
• Cramer’s rule for small linear systems

Vector spaces

• Linear independence
• Span
• Bases and dimension
• Bases change