Vector outer product is denoted by or . Vector outer product is also called vector matrix product because the result of the vector multiplication is a matrix. It can only be performed for two vectors of any size, not necessarily the same size.
Algebraically, the vector outer product is a multiplication of a column vector by a row vector to obtain a matrix provided by the formula below
Suppose we have and , the vector outer products are
Some important properties of vector outer product are
- Vector outer product is a not commutative operation. If you reverse the order you will get different result and even different size .
- If matrix is the results of a vector product then multiplication of that matrix with the second factor produces a vector of the first factor scaled by the square norm of the second factor .