- For a $1 \times n$ or $n \times 1$ vector, I remember people say it is n-dimensional.
For a $n \times m$ matrix, I heard it is said to have size $n \times m$. As to its dimension, quoted from Wikipedia:
a linear map can be represented by a matrix, a 2-dimensional array, and therefore is a 2nd-order tensor. A vector can be represented as a 1-dimensional array and is a 1st-order tensor. Scalars are single numbers and are zeroth-order tensors.
So is it right that there are two different ways to interpret the dimension of a multidimensional array: one is the dimension of the vector space of the arrays, and the other is ( I don't know how to describe). For example,
- the dimension of a $1 \times n$ or $n \times 1$ vector can be said to be either $n$ or $1$;
- the dimension of a $n \times m$ matrix can be said to be $n * m$ as well as $2$?
If yes, I wonder what cases to use which way and not cause confusion?