3 ms·
> Abstractly, a vector is neither a row nor a column. An n-dimensional vector is an ordered collection of n coordinates. An m by n matrix is an m-dimensional ve
by VyseofArcadia 4y ago
> Abstractly, a vector is neither a row nor a column. An n-dimensional vector is an ordered collection of n coordinates. An m by n matrix is an m-dimensional vector of n-dimensional vectors.
Oh we can get more abstract than that.
A vector is an element of a vector space, or, if you'd like, an F-module where F is a field. A matrix is a homomorphism between vector spaces.
- panda-giddiness 4y agoTo give an explicit example that breaks the column-vector mold: the set of 2x2 matrices with real entries forms a vector space, where each vector is a 2x2 matrix.
- VyseofArcadia 4y agoLet's get even weirder and leave finite dimensions behind. The set of sequences of complex numbers z_n such that the infinite sum from i = 1 to infinity of |z_i|^2 converges.