### General Information

Course Code | X_400649 |
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Credits | 6 EC |

Period | P4 |

Course Level | 200 |

Language of Tuition | English |

Faculty | Faculty of Science |

Course Coordinator | dr. R. Hindriks |

Examiner | prof. dr. S. Bhulai |

Teaching Staff |
dr. R. Hindriks |

### Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods | Seminar, Lecture, Practical |
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Target audiences

This course is also available as:

### Course Objective

Besides to be able to explain, interrelate, know the basic propertiesof, and construct simple arguments with the concepts listed above, the

student will learn the following skills (organized

by topic):

Linear systems:

Can solve systems of linear equations using row-reduction

Can determine the number of solutions of a linear system

Can prove or disprove simple statements concerning linear systems

Linear transformations:

Can determine if a linear transformation is one-to-one and onto

Can compute the standard matrix of a linear transformation

Can use row-reduction to compute the inverse of a matrix

Can prove or disprove simple statements concerning linear

transformations

Subspaces and bases

Can compute bases for the row and column space of a matrix

Can compute the dimension and determine a basis of a subspace

Can prove or disprove simple statements concerning linear systems

Eigenvalues and eigenvectors

Can compute the eigenvalues of a matrix using the characteristic

equation

Can compute bases for the eigenspaces of a matrix

Can diagonalize a matrix

Can prove or disprove simple statements concerning eigenvalues and

eigenvectors

Orthogonality

Can compute the orthogonal projection onto a subspace

Can determine an orthonormal basis for a subspace using the

Gramm-Schmidt algorithm

Can solve least-squares problems using an orthogonal projection

Can orthogonally diagonalize a symmetric matrix

Can compute a singular value decomposition of a matrix

Can prove or disprove simple statements concerning orthogonality

### Course Content

The topics that will be treated are listed below. For every topic, therelevant concepts are listed.

Linear systems:

linear system (consistent/inconsistent/homogeneous/inhomogeneous),

(augmented) coefficient matrix, row equivalence, pivot position/column,

(reduced) echelon form, basic/free variable, spanning set, parametric

vector form, linear (in)dependence.

Linear transformations:

linear transformation, (co)domain, range and image, standard matrix,

one-to-one and onto, singularity, determinant, elementary matrices.

Subspaces and bases:

subspace, column and null space, basis, coordinate system, dimension,

rank.

Eigenvalues and eigenvectors:

eigenvalue, eigenvector, eigenspace, characteristic equation/polynomial,

algebraic multiplicity, similarity, diagonalization and

diagonalizability.

Orthogonality:

dot product, norm, distance, orthogonality, orthogonal complement,

orthogonal set/basis, orthogonal projection, orthonormality, orthonormal

basis, Gramm-Schmidt process, least squares problem/solution, orthogonal

diagonalization, singular value/vector, singular value decomposition,

Moore-Penrose inverse.

### Teaching Methods

The course is spread over a period of seven weeks. Each week there willbe two theoretical classes of 90 minutes each and

two exercise classes of 90 minutes each.

### Method of Assessment

There is a written exam at the end of the course.### Entry Requirements

None.### Literature

Linear Algebra and its Applications, by David C. Lay, Steven R. Lay enJudi J. McDonald, global edition (fifth edition), Pearson.