You know complex numbers and their arithmetic operations in their various representations.
You are familiar with geometric calculus. You are able to compute norm, inner products, orthogonal projection, and cross product of vectors and use vectors to describe geometric objects.
You are able to recognize systems of linear equations and use suitable methods to solve them. In addition, you can apply the linear least square method to overdetermined systems of linear equations.
You are familiar with the basic operations of matrix calculus. These include the calculation of matrix products, determinants, inverse matrices, etc
Real Numbers and Introduction to Complex Numbers
Number sets: real numbers and field axioms
Complex numbers and the complex plane
Calculus with complex numbers (summation and multiplication)
Polar form of complex numbers (polar coordinates, modulus and argument)
Euler‘s formula and exponential form of complex numbers
Powers and roots of complex numbers
Vector Calculus
Vectors in R^2 and R^3
Norm of a vector, inner product and angle between vectors
Orthogonal Projection
Parametric representations of lines and planes in R^3
Cross Product of vectors
Matrix Calculus
Matrices and matrix product
Solution of systems of linear equations, Gauss elimination and row echelon form
LU decomposition
Linear least squares
Inverse Matrix
Determinant
Lernbuch Lineare Algebra und Analytische Geometrie, Gerd Fischer, Florian Quiring, Springer Spektrum Verlag, 2. Auflage http://dx.doi.org/10.1007/978-3-8348-2379-3
Lineare Algebra für Naturwissenschaftler und Ingenieure, Michael Ruhrländer, Pearson Studium ISBN 978-3-86894-271-2
Formeln, Tabellen, Begriffe Mathematik - Physik - Chemie Orell Füssli Verlag, ISBN 978-3-280-04029-4