The course aims to introduce the basic techniques of linear algebra, which is a fundamental tool in most applications of mathematics: matrices, Gauss elimination, vector spaces, inner products, determinants, eigenvalues and eigenvectors.
At the end of the course, the students will be able to apply linear algebra techniques to the solution of problems about matrix decompositions, analysis of linear maps, orthogonalization and computation of eigenvalues and eigenvectors.
Knowledge and understanding: students will master the fundamental notions of linear algebra and matrix theory.
Applying knowledge and understanding: the students will be able to analyze and model problems in a rigorous way and to recognize applicability of linear algebra to various situations.
Making judgements: the students will be able to choose among the various techniques the one better suited to the problem at hand.
Communication skills: the students will be able to describe the solution of a problem employing correct terminology.
Learning skills: the students will be able to widen 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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