THE COURSE AIMS TO PROVIDE AN INTRODUCTION TO THOSE ASPECTS OF LINEAR MATHEMATICS AND GEOMETRY NEEDED IN SCIENCE AND ENGINEERING
teacher profile teaching materials
2- Rows by columns product of matrices; invertible matrices; rank of a matrix; Rouche'-Capelli Theorem.
3- Geometrical vectors. Vector spaces. Subspaces. Generating vectors and linearly independent vectors.
4- Basis of a vector space: dimension of a vector space; Grassmann's formula.
5- Linear applications: Kernel and image of a inear application. Dimension of Kernel and Image of a linear application.
6- Matrix associated to a linear application. Diagonalization of linear operators.
Programme
1- Linear systems: matrix associated to a linear system; sum of matrices and multiplication by real numbers; reduced matrices; Gauss-Jordan algorithm.2- Rows by columns product of matrices; invertible matrices; rank of a matrix; Rouche'-Capelli Theorem.
3- Geometrical vectors. Vector spaces. Subspaces. Generating vectors and linearly independent vectors.
4- Basis of a vector space: dimension of a vector space; Grassmann's formula.
5- Linear applications: Kernel and image of a inear application. Dimension of Kernel and Image of a linear application.
6- Matrix associated to a linear application. Diagonalization of linear operators.
Core Documentation
S. Lang: "Linear Algebra" - Springer edType of evaluation
Written exam with exercises on the arguments of the course; in particular: linear systems, rank of a matrix, dimension of vector spaces, linear applications, diagonalization of linear operators