## Learning objectives

To acquire the notions of linear geometry in R^3, Linear algebra, abstract vector spaces, linear maps.

To acquire and improve logical and abstract reasoning and problem solving skills

## Prerequisites

Trigonometry, Solving linear and quadratic equations, solving linear systems.

## Course unit content

Vectors, Geometry in R^3, Vector Spaces, Matrices

## Full programme

Vectors in R^3: basic operations; scalar product; cross product.

R^2 and R^3 geometry: lines in R^2; mutual position of two lines in R^2; lines in R^3; planes in R^3; mutual position of two lines in R^3; mutual position of two planes in R^3; mutual position of a line and a plane in R^3.

Matrices: basic operations; square matrices and determinant; the inverse of a square matrix; rank; orthogonal and unitary matrices; change of coordinates matrix.

Linear systems: compatibility and resolution; Rouche-Capelli Theorem and applications to 3D geometry.

Complex numbers: cartesian and trigonometric description.

Vector spaces: definition and examples; linear dependence; vector subspaces; basis and coordinates; intersection and sum of subspaces; scalar product; orthonormal sets and basis; Gram-Schmidt algorithm.

Linear maps and diagonalization: representing matrices; kernel and image of a linear map; eigenvalues and eigenvectors; condition to diagonalize an endomorphism; Spectral Theorem.

## Bibliography

M. Abate, C. De Fabritiis, Geometria analitica con elementi di algebra lineare, 2a ed., Mc Graw-Hill, 2010.

L. Alessandrini, L. Nicolodi, Geometria e algebra lineare. Con esercizi svolti. Ed. Uninova.

G. Catino, S. Mongodi, Esercizi svolti di Geometria e Algebra Lineare, Società editrice Esculapio.

## Teaching methods

Live classes, exercises sessions, homework, studying from the book and from the handouts

## Assessment methods and criteria

There will be tests towards the half of the semester and in the end of the semester. The exam will be both written and oral if it will be possible to do exams in a classroom, otherwise it will be an online test.

## Other information

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