# GEOMETRY (UNIT 1)

## LEARNING OUTCOMES OF THE COURSE UNIT

The course aims to provide knowledge and techniques of linear algebra for the purpuse of providing tools for resolving linear systems, diagonalising matrices and simply describing the behaviours of geometric bodies in the plane and in space.

## COURSE CONTENTS SUMMARY

Field of complex numbers: trigonometric and exponential form.Vector and matrix calculus. Determinant and rank of a matrix. Linear systems. Real and complex vector spaces. Bases and dimension. Sum and direct sum of subspaces: Grasmann relation. Linear applications and associated matrices.Eigenvalues and eigenvectors. Diagonalizability of a matrix. Bilinear forms and scalar products. Orthonormal bases. Real symmetrical matrices: diagonalizability. Orthogonal matrices and isometries. Coordination in the plane and in the space. Parametric and cartesian representation of stright lines and planes.Parallelism and orthogonality.

## RECOMMENDED READINGS

Marco Abate " GEometria" MacGraw-Hill

## ASSESSMENT METHODS AND CRITERIA

Verification of learning takes place through a written test and an oral. In the written examination through the exercises proposed by the student must demonstrate that they possess the basica knowledge of ilinear algebra and analytical geometry. In the oral examination the student must be able to conduct its own demonstrations relating to the themes of the course using an appropriate language and mathematical formalism.

## TEACHING METHODS

Privileged education mode is the frontal lesson that offered arguments from a formal point of view, accompanied by significant examples, applications and exercise.