Geometry 1

A.y. 2018/2019
7
Max ECTS
60
Overall hours
SSD
MAT/03
Language
Italian
Learning objectives
The course aims to provide students with the basic tools of linear algebra, in particular with the properties of vector spaces (possibly equipped with a scalar product) and linear maps between real and complex spaces.
Expected learning outcomes
Undefined
Course syllabus and organization

CORSO A

Responsible
Lesson period
Second semester
Course syllabus
GEOMETRY 1


The course covers the basics of linear algebra:

-- definition of vector spaces and subspaces (over the real numbers and the complex numbers);

-- notion of basis and dimension of a vector space. The Grassmann formula;

-- linear maps and associated matrices. The rank of a matrix;

-- linear systems. Structure of the space of solutions. The Gauss--Jordan method;

-- determinant. Invertible matrices;

-- characteristic polynomial, eigenspaces and eigenvectors of an endomorphism;

-- scalar and hermitian products, orthogonal bases, the Gram--Schmidt method;

-- notions of angle and length via scalar products;

-- the spectral theorem (over the reals and the complex numbers);

-- bilinear forms. The theorems of Sylvester and Lagrange.
MAT/03 - GEOMETRY - University credits: 7
Practicals: 20 hours
Lessons: 40 hours

CORSO B

Responsible
Lesson period
Second semester
Course syllabus
GEOMETRY 1


The course covers the basics of linear algebra:

-- definition of vector spaces and subspaces (over the real numbers and the complex numbers);

-- notion of basis and dimension of a vector space. The Grassmann formula;

-- linear maps and associated matrices. The rank of a matrix;

-- linear systems. Structure of the space of solutions. The Gauss--Jordan method;

-- determinant. Invertible matrices;

-- characteristic polynomial, eigenspaces and eigenvectors of an endomorphism;

-- scalar and hermitian products, orthogonal bases, the Gram--Schmidt method;

-- notions of angle and length via scalar products;

-- the spectral theorem (over the reals and the complex numbers);

-- bilinear forms. The theorems of Sylvester and Lagrange.
MAT/03 - GEOMETRY - University credits: 7
Practicals: 20 hours
Lessons: 40 hours
Professor(s)
Reception:
by appointment (by e-mail)
Math. Dept. - via C. Saldini 50 - Milano