The course introduces the basic techniques of linear algebra, which is a fundamental tool in most applications of mathematics. At the end of the course, the students will be able to analyze and model problems in a rigorous way and to recognize applicability of linear algebra in different contexts. In particular, they will be able to employ tools and techniques of linear algebra to solve problems of matrix decompositions, analysis of linear maps, orthogonalization and computation of eigenvalues and eigenvectors. The students will be able to precisely describe the solution of a problem employing the appropriate terminology. Moreover, they will acquire adequate confidence on the topics studied that will allow them to independently deepen their knowledge starting from what they learned.
Linear systems and matrices
Gauss elimination and LU decomposition
Vector spaces and linear maps
Bases and matrix representation of linear maps
Inner products and Gram-Schmidt algorithm
Eigenvalues and eigenvectors, diagonalization of matrices
|E. Gregorio, L. Salce||Algebra Lineare||Libreria Progetto Padova||2005|
The written exam consists in discussing a topic from a theoretical point of view and in solving some exercises on the topics of the course.
The complete solution of the exercises leads to a grade not higher than 21/30.
• Knowledge and understanding: comprehension of the text of the problems and mastering of the theory behind them.
• Applying knowledge and understanding: ability to apply the general techniques to a specific problem
• Making judgements: ability to express the learned theoretical concepts in varied situations
• Communication skills: language clarity and appropriateness
• Learning skills: ability to structure a proof different from those presented during the course
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