Everyone who studies elementary linear algebra encounters the concepts of row rank and column rank of a matrix at some point. Interestingly, it turns out that they are always equal. Although this is not difficult to prove, it often remains somewhat of a mystery: Why is this true? The aim of this course is to present a surprisingly ostensive answer to this question for matrices over the real numbers.

Everyone can follow the explanations, including those who have never heard of the rank of a matrix, since we introduce all needed concepts on an intuitive level. For all who are already familiar with the terminology, we also include formal proofs based on the intuitive arguments.