The aim of the course is to provide working knowledge of methods and tools of linear algebra that are necessary in the study of economic, financial and organisational subjects. At the end of the course, students will be able to carry out exercises adapting the methods learned and to argue the relevance of the main theoretical results discussed in class.

Knowledge and understanding: The course will provide many basic mathematical tools, together with their theoretical interpretation and examples of their possible applications to quantitative analysis in Economics, Finance, Statistics, possibly also using MATLAB software. Ability to apply knowledge and understanding: Students will be able to adapt and apply a variety of techniques to solve non-standard mathematical problems, as well as to discuss the arguments that justify the use of such techniques. Autonomy of judgement: Students must be able to correctly choose the best solution strategy for each mathematical problem and understand how to apply concepts and tools to economic and financial problems. This ability will be assessed through exercises and examinations. Communication skills: Students will learn to formulate and communicate mathematical concepts and logical reasoning, using the English language. They will be able to understand how different concrete problems can be studied using similar techniques. Learning skills: Students will expand their mathematical knowledge and reasoning and become able to work independently with advanced mathematical concepts and tools; they will also learn the basics of the MATLAB language.

An introduction to linear algebra, with economic applications. Matrices, systems of linear equations, spaces, subspaces and bases, eigenvalues and eigenvectors, orthogonality, least squares, principal component analysis, Markov chains, linear programming.

R.Larson, Elementary Linear Algebra, 8th edition, Cengage "Mathematics for Economists" di Simon and Blume, edizioni Norton (International Student Edition) “Exploring linear algebra with Matlab, labs and projects with Matlab”, Crista Arangala Further reading material will be provided on the official course's web page, via the learn.luiss.it platform.

Theoretical lectures on each topic, accompanied by examples and short exercises. Weekly exercises: Written and Matlab exercises. Study material will be provided to students a few days in advance of the lecture and then carried out in class. Student participation in the exercises will be encouraged

The examination consists of a written exam followed by an oral examination. Each written exam will consist of two parts: quizzes and written exercises. The student must provide solutions to the exercises by adequately arguing and demonstrating thorough knowledge of the theoretical results used, using appropriate mathematical language. Students will take a midterm exam in the middle of the course; in case of passing the midterm, the student is allowed to take the final written exam only on the topics of the second part of the course. Students are admitted to the oral exam with a grade greater than or equal to 16. The oral exam is mandatory for both students who intend to obtain a final grade greater than (or equal to) 27 and students who did not obtain a sufficient grade on the written exam (i.e., whose grade is above or equal to 16 and below 18). The examination for the two categories of students will be different. Students who aspire to a grade greater than or equal to 27 will be given an exercise to do with Matlab one day before the oral exam, which will form the basis of the oral interview. For students who did not achieve a passing grade, the oral test will cover the entire theoretical program of the course.

Teacher interview