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## Linear Algebra

2019-2020

### Course Objective

Besides to be able to explain, interrelate, know the basic properties
of, 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, the
relevant 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 will
be 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.

None.

### Literature

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

### Target Audience

IMM2, LI2, and CS2

None.

### General Information

Course Code X_400649 6 EC P4 200 English Faculty of Science dr. R. Hindriks dr. R. Hindriks 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
Target audiences

This course is also available as: