LINEAR ALGEBRA AND GEOMETRY F - N

Academic Year 2024/2025 - Teacher: Dino FESTI

Expected Learning Outcomes

Knowledge: being able to compute the rank of a matrix, with or without a parameter, to study a vector space, to study a linear application, to determine eigenvalues and eigenspaces of an endomorphism, to diagonalize a matrix, to solve problems of linear geometry, to classify conics and quadrics and to study conics bundles in the plane.

Understanding: fundamental definitions and theorems about vector spaces, linear applications and endomorphisms, constructions and theorems about lines and planes in the space and conics in the plane, definitions and theorems about the classifications of quadrics.

Required Prerequisites

Polynomial equations and disequalities of degree at most 3. Factorization of polynomials in special cases. Sine, cosine and tan functions with values at notable degrees. Square root and absolute value of real numbers. Basic logic and basic set theory.

Attendance of Lessons

The student is supposed to attend at least 70% of the total amount of hours of the course. Attendance in in any case strongly suggested in order to pass the exam.

Detailed Course Content

Textbook Information

1. S. Lang, Introduction to linear algebra. Springer; 2nd edition, 1985.

Learning Assessment

Learning Assessment Procedures

EXAM: the exam consists of a written test (usually 90 minutes) and, upon passing the written test, an oral examination. The written test consists of one or more open questions about the Linear Algebra and the Geometry parts.
Should the necessity arise, it will be possible to take the test also remotely. In this case, the duration of the written test may vary. 

Examples of frequently asked questions and / or exercises