11781 - Linear Algebra

Course contents

Systems of linear equations in n unknowns; geometric interpretation for n=2,3. Matrices of a linear system; triangularization process. Non-singular matrices. Matrix multiplication; matrix representation of a linear system. Non-singular matrices as invertible matrices. Gauss-Jordan algorithm. Eigenvectors and eigenvalues; application to the computation of the powers of a matrix. Matrix algebra. Determinant, Laplace expansions, characteristic properties. Cramer rule. Non-singular matrices as matrices with non-zero determinant. Eigenvalues and characteristic polynomial. Vector space R^n; geometric interpretation for n=2,3. Vector representation of a linear system. Linearly independent sets and bases of R^n. Euclidean inner product, norm, orthogonality in R^n; geometric interpretation for n=2,3. Pythagoras theorem. Fourier coefficients; orthogonal projection of a vector on a subspace. Least squares solutions of a linear system.

Furter informations: http://www.dm.unibo.it/~regonati/rimini.html

Readings/Bibliography

Teaching material will be available to the web page

http://www.dm.unibo.it/~regonati/rimini.html

Teaching methods

classroom lectures

Assessment methods

Algebra Lineare and Analisi Matematica are the two parts of Matematica (corso integrato).
The exam of Matematica consists of a written test and an oral test.
The written test consists of some exercises about the two parts of the corso integrato. During the written test students are not allowed to use notes or books. The aim of the oral test is to verify students' understanding of the concepts of the two parts of the corso integrato  and their ability to express these concepts correctly.

The final grade is established on the base of an overall judgement on the oral and written tests.

Links to further information

http://www.dm.unibo.it/~regonati/rimini.html

Office hours

See the website of Francesco Regonati