Course content

Please familiarise yourself with the course information (link above).

Toepassings van lineÍre stelsels. LineÍre transformasies. Projeksie-, rotasie- en refleksiematrikse. (2D/3D). CAD-toepassings. Vektorruimtes. Verskilvergelykings. Kleinste kwadrate benaderings. Eiewaardes en -vektore. Applications of linear equations. Linear transformations. Projection, rotation and reflection matrices (2D/3D). CAD-applications. Vector spaces. Difference equations. Least squares approximations. Eigenvalues and vectors.

Lecture summary

Klasnotas / Class notes
15/09Motivation: Millau Viaduct. Linear algebra terminology: matrices, row vectors, column vectors. Matrix algebra with focus on multiplication (see also Gilbert Strang's lecture--the link to MIT Open Courseware is to the side). Matrix zoo. Reminder of identities (order of multiplication is especially important!). Brief detour: the meaning of the inverse, and why we don't compute it.
16/09Other uses of matrices: predicting the spread of wildfires. Gaussian elimination: row-reduction as executed by a computer. Three scenarios: unique solution, no solution or free variable. Examples: closed economy, balancing of chemical equations. Homework: traffic network example.
17/09Gaussian elimination: currents in an electric circuit. Overview of LU decomposition (class example).
20/09Linear transformations. Application, reversal and the existence of. Linearity. Geometrical interpretation (projection, shear, translation, dilation, rotation). Simple self-test: addition | multiplication.
22/09Given a description of a linear transformation, determine the corresponding transformation matrix. The technique is simple: AI = A = [Ae1 Ae2 Ae3] (i.e. if you can transform the unit axes, then you know A). Derivation of the rotation matrix in 2D (example spreadsheet). [Extra: Bullet Time]
23/09A closer look at rotation, projection and reflection matrices.


21/09Matrix multiplication, solution of linear systems, introduction to linear transformations. | Memo | Test | Test memo

Freely available textbooks


Zill & Cullen Voorblad

Prescribed textbook, Zill & Cullen (3rd ed).

Outside links