(SOLVED) 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,
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.