Let $F$ be a field. The set $F^n$ of all vectors with $n$ coordinates (which we are going to identify with the set $M_{n\times 1}(F)$ of all single-column matrices with $n$ rows over the field $F$) together with the matrix addition $”+”$ constitutes an Abelian group, i.e. $(F_n, +)$ follows the rules:
|
|
|
|
| created: 2020-11-29 14:23:13 | modified: 2020-11-29 14:24:58 | by: bookofproofs | references: [8684]
[8684] Axler, Sheldon: “Linear Algebra Done Right”, Springer, 2015, 3rd