The student should acquire the background in linear algebra needed to understand and apply concepts and techniques for the solution of problems arising in the different areas of aerospace engineering. A) Learning objectives - To solve systems of linear equations and to interpret the results - To determine whether a square matrix is invertible or not, and to compute the inverse matrix (if it exists) - To understand the notion of bases and coordinates in a vector space - To represent a linear transformation by a matrix - To compute the image and kernel of a linear transformation - To compute the eigenvalues and eigenvectors of a matrix - To compute the SVD decomposition of a matrix - To find an approximate solution to an overdetermined system by least-square fitting B) Specific skills - To be able to solve systems of linear equations - To be able to model real-world problems using linear algebra techniques, and solve them using algorithmic procedures. - To be able to handle the abstract properties of vector spaces. C) General skills - To be able to think abstractly, and to use induction and deduction. - To be able to communicate in oral and written forms using appropriately mathematical language. - To be able to model a real situation using linear algebra techniques. - To be able to interpret a mathematical solution of a given problem, its accuracy, and its limitations. - To be able to use mathematical software.

CB1: Students have demonstrated possession and understanding of knowledge in an area of study that builds on the foundation of general secondary education, and is usually at a level that, while relying on advanced textbooks, also includes some aspects that involve knowledge from the cutting edge of their field of study. CE.FB1: Ability to solve mathematical problems that may arise in engineering. Ability to apply knowledge of: linear algebra; geometry; differential geometry; differential and integral calculus; differential and partial differential equations; numerical methods; numerical algorithms; statistics and optimisation. RA1: Have basic knowledge and understanding of mathematics, basic sciences, and engineering within the aerospace field, including: behaviour of structures; thermodynamic cycles and fluid mechanics; the air navigation system, air traffic, and coordination with other means of transport; aerodynamic forces; flight dynamics; materials for aerospace use; manufacturing processes; airport infrastructures and buildings. In addition to a specific knowledge and understanding of the specific aircraft and aero-engine technologies in each of the subjects included in this degree.

0. Complex Numbers 1. Systems of Linear Equations 2. Vector spaces 3. Matrix Algebra 4. Linear transformations 5. Basis 6. Orthogonality and Least-Squares 7. Eigenvalues and Eigenvectors 8. Pseudoinverse and singular value decomposition

Lecture sessions: 3 credits Problem sessions: 3 credits