# (SOLVED) Outer Product

Discipline: Mathematics

Type of Paper: Question-Answer

Academic Level: Undergrad. (yrs 3-4)

Paper Format: APA

Pages: 1 Words: 275

Question

Outer Product

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=uvT. The outer product is same as the matrix multiplication uvT also 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, vT = [7 2 3 1].

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.