Knowledge

The student...

knows and understands fundamental matrix calculations including addition, multiplication, transposing, inverting and determinants
knows and understands complex numbers
knows and understands use linear and affine transforms, focusing on geometric transformations such as translation and rotation
knows and understands various descriptions of rotation and orientation, such as rotation matrices, euler angles, rotation vectors, axis-angle-representation and quaternions.
knows and understands methods to convert between these representations of rotation and orientation.
knows and understands homogenous vectors and matrices especially matrices for central projection.
knows and understands methods for solving linear equations, such as Gauss-elimination and matrix inversion.
knows and understandsusing scalar product and matrix for projections and approximations as well as the least squares method.
knows and understands barycentric coordinates and interpolation in triangles, as well as the usage of this for 3d-graphics such as Pong-shading and texturing.
knows and understands various applications of linear algebra, such as interpolation of curves and linear regression using least squares

Skills

The student...

is able to solve geometric problems by applying theories for vectors, matrices and linear equations, within the fields listed under "knowledge" above
is able to combine and alternate between different coordinate systems such as model coordinates, world coordinates, camera coordinates and screen coordinates
is able to apply linear algebra to selected problems

General competence

The student...

has acquired a good overview of vector geometry and basic linear algebra with applications, within the fields listed under "knowledge" above
are prepared for learning graphics programming
can develop their general mathematical abilities

Subject description RF5100

Linear Algebra