Content deleted Content added
m →Matrices: re Algebra over a field |
|||
Line 50:
==Matrices==
Let '''F'''<sup>''m''×''n''</sup> denote the set of ''m''×''n'' [[matrix (mathematics)|matrices]] with entries in '''F'''. Then '''F'''<sup>''m''×''n''</sup> is a vector space over '''F'''. Vector addition is just matrix addition and scalar multiplication is defined in the obvious way (by multiplying each entry by the same scalar). The zero vector is just the [[zero matrix]]. The [[dimension (vector space)|dimension]] of '''F'''<sup>''m''×''n''</sup> is ''mn''. One possible choice of basis is the matrices with a single entry equal to 1 and all other entries 0.
When ''m'' = ''n'' the [[square matrix|matrix is square]] and [[matrix multiplication]] of two such matrices produces a third. This vector space of dimension ''n''<sup>2</sup> forms an [[algebra over a field]].
==Polynomial vector spaces==
| |||