Vector Outer Product

Vector outer product is denoted by Outer Product or Outer Product . 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 Outer Product to obtain a matrix provided by the formula below

Outer Product
Example
Suppose we have Outer Product and Outer Product , the vector outer products are
Outer Product
Outer Product

Properties

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 Outer Product .
  • If matrix is the results of a vector product Outer 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 Outer Product .

Originally from http://people.revoledu.com/kardi/tutorial/LinearAlgebra/VectorOuterProduct.html

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