The space R^n of n-tuples of real numbers. Matrices and their algebraic properties. Linear systems, Gauss algorithm. Standard scalar product and norm in R^n. Complex numbers. Vector spaces, subspaces; linearly independent vectors, generators, bases, dimension. Rank of matrices. Linear maps, kernel, image. Determinant. Eigenvalues and eigenvectors. Diagonalization.
Notes provided by the Teacher.
Recommended reading:
Abate, Algebra Lineare
Nicholson, Algebra Lineare
Robbiano, Algebra Lineare
Learning Objectives
This course provides students with the knowledge of the basic concepts of linear algebra,
starting from the language of matrices, which is important for the subsequent career.
Aquirede Competences (at the end of the course): Basic Concepts of Linear Algebra
Skills acquired (at the end of the course): Use the basic concepts of linear algebra.
Prerequisites
Courses to be used as requirements (required and / or recommended)
Courses required: None
Recommended Courses: None
Teaching Methods
Lectures, tutorials. Intermediate tests will be scheduled during the term.
Type of Assessment
Assemnets Method:
Written Test.
Alternatively it is possible to take advantage of the intermediate tests during the term.
Course program
The space R^n of n-tuples of real numbers. Matrices and their algebraic properties. linear systems, Gauss algorithm. Standard scalar product and norm in R^n. Complex numbers. Vector spaces, subspaces; linearly independent vectors, generators, bases, dimension, coordinates. Space generated by the columns of a matrix, generated by the row space. Rank. Linear maps, kernel, image. Rouche-Capelli and the structure of solutions of a linear system. Linear applications and matrices. Determinant: axiomatic definition of the determinant function, its properties and calculations by elimination of Gauss. Eigenvalues and eigenvectors. Diagonalization, orthogonal diagonalization.