# (SOLVED) Outer Product

**Discipline:** Mathematics

**Type of Paper:** Question-Answer

**Academic Level:** Undergrad. (yrs 3-4)

**Paper Format:** APA

**Pages:**1

**Words:**275

Question

The tensor product of two coordinate vectors is termed as “Outer
product”. This is a special case for “Kronecker product of matrices”.
Let *u* and *v* be vectors. Then, the outer product of *u* and *v* is *w*=*uv ^{T}.* The outer product is same as the matrix multiplication

*uv*also

^{T}*u*is denoted by

*m*× 1 column vector and

*v*is denoted by

*n*× 1 column vector.

Let be two vectors. Then, the outer product of

*u*and

*v*is obtained as follows:

**Properties of an outer product:**

• The result of an outer product is

*m*×

*n*rectangular matrix.

• The outer product is not commutative. That is,

• Multiply the second vector

*v*with the resultant product gives a vector of the first factor

*u*scaled by the square norm of the second factor

*v.*That is,

**Example:**

Consider the vectors .

Transpose of v is,

*v*= [7 2 3 1].

^{T}The outer product of , which is obtained below:

Thus, the outer product is a rectangular 3 × 4 matrix.

Check the outer product is commutative or not.