# MAT-01266 Mathematics 2, 5 cr

Robert Piche

#### Lessons

 Implementation Period Person responsible Requirements 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.

#### Learning Outcomes

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.

#### Content

 Content Core content Complementary knowledge Specialist knowledge 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.

#### Study material

 Type Name Author ISBN URL Additional information Examination material Book Linear Algebra, A Modern Introduction (2nd ed.) Poole Available in library for period-loan. Yes

#### Prerequisites

 Course Mandatory/Advisable Description MAT-01166 Mathematics 1 Mandatory

#### Correspondence of content

There is no equivalence with any other courses

 Updated by: Piche Robert, 27.11.2019