# Linear Algebra and Elements of Geometry (2016/2017)

Course code
4S00253
Credits
12
Coordinator
Lidia Angeleri
Teaching is organised as follows:
ALGEBRA LINEARE 6 MAT/02-ALGEBRA See the unit page See the unit page
ELEMENTI DI GEOMETRIA 6 MAT/03-GEOMETRY II sem. Alberto Benvegnu'
Davide Rinaldi

#### Learning outcomes

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MM: ALGEBRA LINEARE
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First of all, the students are introduced to the language and formal reasoning required for the study of higher mathematics. Furthermore, the main notions and techniques of linear algebra and matrix theory are presented, focussing both on theoretical and computational aspects. Moreover, the course provides an introduction to planar and spatial analytic geometry, within the projective, affine, and euclidean setting. Finally, the main properties of conics will be discussed. Both analytical (coordinates, matrices) and synthetic tools will be employed.
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MM: ELEMENTI DI GEOMETRIA
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First of all, the students are introduced to the language and formal reasoning required for the study of higher mathematics. Furthermore, the main notions and techniques of linear algebra and matrix theory are presented, focussing both on theoretical and computational aspects. Moreover, the course provides an introduction to planar and spatial analytic geometry, within the projective, affine, and euclidean setting. Finally, the main properties of conics will be discussed. Both analytical (coordinates, matrices) and synthetic tools will be employed.

#### Syllabus

Part 1: Groups, fields. The field of complex numbers. Matrices, matrix operations and their properties. Determinant and rank of a matrix. Inverse matrix. Systems of linear equations. The method of Gaussian elimination. Vector spaces, subspaces, bases, dimension. Linear maps.

Part 2: Eigenvalues and eigenvectors. Jordan canonical form. Affine and Euclidean spaces. Lines, planes, hyperplanes. Vector product and mixed product. Affine and isometric transformations. Projective spaces. Geometry of projective plane. Conics.

#### Assessment methods and criteria

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MM: ALGEBRA LINEARE
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The exam consists of: - a joint written examination on the module Linear Algebra and the module Elements of Geometry, - a joint oral examination on both modules. Only students who have passed the written examination will be admitted to the oral examination.
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MM: ELEMENTI DI GEOMETRIA
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see Linear Algebra