87296 - Algebra and Geometry T

Learning outcomes

Basic knowledge of matrix calculus and analytical geometry, framed within linear algebra.

Course contents

Linear algebra

-- Matrices and linear systems.

--- Gauss method for solving linear systems.

--- matrix rank and criteria for solving a linear system.

-- Vector spaces and linear applications

--- Subspaces, bases of vector spaces

--- Dimension of a vector space

--- Linear applications; kernel and image.

--- the matrix associated to a linear application.

-- Endomorphisms.

--- Eigenvalues and Eigenvectors.

--- characteristic polynomial

---linear applications and invertible matrices

--- endomorphisms

-- Bilinear maps and scalar products

--- the matrix associated to a bilinear map

--- scalar products and Euclidean spaces

 

Elements of analytical geometry of the plane and space

--the Euclidean pane and the Euclidean space.

----extension of the plan and the ordinary space

--lines in the plane; Implicit, parametric, and Cartesian form.

---incidence and angle between two lines

--Conics

---conics and associated quadratic forms

---Conditions of tangency between a line and a conic

--- geometrical elements of a conic

--lines and planes in space

--overview of quadrics in the ordinary space.

 

 

 

 

 

 

Readings/Bibliography

-Enrico Schlesinger, Algebra lineare e geometria, Zanichelli

-Luca Mauri e Enrico Schlesinger, Esercizi di algebra lineare e geometria, Zanichelli

Teaching methods

Frontal lessons / online lessons

This course participates in the University's educational innovation project

Assessment methods

The examination consists in the passing of a written test and an oral one.

In the written test the candidate must solve exercises using the skills acquired in the course.

In the oral test the candidate must show that he has assimilated the concepts and skills provided by the course.

 

Office hours

See the website of Sergio Venturini