This course "Application of Linear Algebra'' is band on the lectures given of the late by the author to the postgraduate students at Tallinn Technical University. Our aim was to acquaint the students with the linear algebra packages LINPACK, EISPACK and LAPACK, and with the theoretical fundamentals of the parts of the packages MATLAB, MAPLE, MATHCAD and MATHEMATICA related to linear algebra. We have tried to explain the linear algebra methods which form the base for the computing methods used in the packages. We would like to stress that the aim of the course is not to work out concrete computing algorithms but to learn about the basic ideas related to these algorithms. It will be assumed that the reader is acquainted with the basic ideas of algebra.