|cv, cm, etc.||multiply each element by a scalar|
|u.v, v.m, m.v, m1.m2, etc.||vector and matrix multiplication|
|Cross[u,v]||vector cross product (also input as u×v)|
It is important to realize that you can use "dot" for both left‐ and right‐multiplication of vectors by matrices. The Wolfram Language makes no distinction between "row" and "column" vectors. Dot carries out whatever operation is possible. (In formal terms, contracts the last index of the tensor with the first index of .)
For some purposes, you may need to represent vectors and matrices symbolically without explicitly giving their elements. You can use Dot to represent multiplication of such symbolic objects.
The "dot" operator gives "inner products" of vectors, matrices, and so on. In more advanced calculations, you may also need to construct outer or Kronecker products of vectors and matrices. You can use the general function Outer or KroneckerProduct to do this.
Outer products are discussed in more detail in "Tensors".