Geometry 1
A.Y. 2018/2019
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
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
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.
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
Lessons: 40 hours
Professors:
Gori Anna, Mastrolia Paolo
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.
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
Lessons: 40 hours
Professors:
Tasin Luca, Turrini Cristina
Professor(s)
Reception:
Appointment via email.
Dipartimento di Matematica "F. Enriques" - Ufficio 0.007
Reception:
by appointment (by e-mail)
Math. Dept. - via C. Saldini 50 - Milano