Learning outcomes of the course unit
The course aims to provide basic knowledge and techniques of linear algebra for the purpose of providing tools for resolving linear systems, diagonalising matrices anf simply desbribing the behaviour 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 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. References and coordination in the plane and in space. Parametric and cartesian representation of straight lines and planes. Parallelism and orthogonality. Distances and angles. Reference changes.
F. Capocasa, C. Medori: "Algebra lineare e Geometria"
A. Abate, C. de Fabritiis: "Geometria analitica con elementi di algebra" P, de Bartolomeis: "Algebra Lineare"