Similar to the introduced matrices, in the following definition, we introduce the notion of a "vector" from a pure notational perspective as a special case of a matrix.

Definition: Column Vectors and Row Vectors

Let $n\ge 1$ be a natural number. A column vector (or just vector) with $n$ field elements is a matrix over a field $F$ with just one column and many rows, i.e. an element of $M_{m\times 1}(F):$


Similarly, a row vector is transposed column vector


A row vector is an element of $M_{1\times m}(F)$.


Chapters: 1
Corollaries: 2
Definitions: 3 4 5
Proofs: 6

Thank you to the contributors under CC BY-SA 4.0!




  1. Knabner, P; Barth, W.: "Lineare Algebra - Grundlagen und Anwendungen", Springer Spektrum, 2013