Linear Algebra and geometry

Course objectives

General goals: To learn basic Linear Algebra and Geometry. Specific goals: Vector spaces, dimension, linear maps, isomorphisms, matrices, elementary operations, reduction to a row echelon matrix. Affine spaces, affine maps, affine coordinates.Determinant, Laplace, Binet, Cramer.Diagonalization, eigenvalues, eigenspaces. Positive definite real scalar product. Knowledge and understanding: The student will learn basic Linear Algebra and Geometry. Applying knowledge and understanding: The student will learn to apply Linear Algebra and Geometry in order to solve problems. Critical and judgmental abilities: The student will learn when Linear Algebra and Geometry are relevant for the solution of a problem. Communication skills: The student will learn to communicate using the language of Linear Algebra and Geometry. Learning ability: The student will be able to understand results in Linear Algebra and Geometry.

Channel 1
KIERAN GREGORY O'GRADY Lecturers' profile

Program - Frequency - Exams

Course program
Sets, functions, relations. Complex numbers. Vector spaces. Subspaces, linear (in)dependence, bases. Dimension of a vector space. Grassmann's formula. Affine coordinates. Affine spaces. Linear combinations of points, affine subspaces. Linear maps. Image and kernel of a linear map. Isomorphisms. Matrices, product of matrices. Matrix associated to linear map. Elementary operations on the rows of a matrix: reduction to a row echelon matrix. Dual of a vector space. Elementary operations: resolution of a system of linear equations, computation of the inverse. Change of basis matrix, coniugation. Affine maps, change of affine coordinates. Cartesian equations of affine subspaces. Definition of determinant. Multilinear and alternating maps, properties of the determinant. Laplace. Binet's formula. Permutations and determinant. Cramer. Quadratic forms. Bilinear forms, non-degenerate forms. Symmetric bilinear forms and quadratic formes, associated matrices. Orthogonality. Diagonalization of simmetriche bilinear forms (and quadratic forms). Diagonalization. Eigenvalues, eigenspaces. Positive definite real scalar product.
Prerequisites
High school Mathematics courses
Books
Marco Abate, Chiara De Fabritiis. Geometria analitica con elementi di algebra lineare. McGraw-Hill Education
Frequency
Not compulsory.
Exam mode
Written and oral exam.
Lesson mode
The teacher explains, with the aid of the blackboard, trying to stimulating active participation by the students.
Channel 2
  • Lesson code10621298
  • Academic year2025/2026
  • Coursecorso|33503
  • CurriculumCurriculum unico
  • Year1st year
  • Semester2nd semester
  • SSDMAT/02
  • CFU6
  • Subject areaFormazione matematico-fisica