# MAT-01266 Mathematics 2, 5 cr

Robert Piche

#### Opetus

 Toteutuskerta Periodi Vastuuhenkilö Suoritusvaatimukset MAT-01266 2019-01 2 Dmytro Baidiuk Robert Piche Jaakko Pihlajasalo Final exam, homework, weekly exercises, and MATLAB Fundamentals self-paced training course in MATLAB Academy.

#### Osaamistavoitteet

In this course the student learns the basic theory and methods of linear algebra and matrix analysis. The student learns how to prove theorems and solve problems using mathematical methods and to present solutions orally and in written form.

#### Sisältö

 Sisältö Ydinsisältö Täydentävä tietämys Erityistietämys 1. Vectors in R^n: the dot product, length, angle, orthogonality, and projection onto a vector. Lines and planes. 2. Systems of linear equations: solving using Gaussian elimination. Gauss-Jordan method. Row equivalence. 3. Spanning sets and linear independence, subspaces, basis, rank, and dimension. 4. Matrices: matrix algebra, matrix product, the transpose, the inverse, the determinant, the cross product. Eigenvalues and eigenvectors. Different representations of matrix product. Linear transformation and the standard matrix. The scalar triple product. Similarity and diagonalization. Markov chains 5. Orthogonality, orthogonal matrices, orthogonal complement, orthogonal projection. Least squares approximation. Gram-Schmidt process. Orthogonal diagonalization. The four fundamental spaces of a matrix. 6. Basic competence in using Matlab to solve mathematical problems.

#### Oppimateriaali

 Tyyppi Nimi Tekijä ISBN URL Lisätiedot Tenttimateriaali Book Linear Algebra, A Modern Introduction (2nd ed.) Poole Available in library for period-loan. Yes

#### Esitietovaatimukset

 Opintojakso P/S Selite MAT-01166 Mathematics 1 Mandatory

#### Vastaavuudet

Opintojakso ei vastaan mitään toista opintojaksoa

 Päivittäjä: Piche Robert, 27.11.2019