# Taking outer product of two matrices

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I have a 3x3 displacement matrix (let us call it u). The displacement gradient tensor F is given by

F = I + ∇ ⊗ u

where,

I = identity matrix

∇ = gradient operator

Can someone help me code this in MATLAB?

##### 11 Comments

Umar
on 15 Jul 2024

Hi @Stephen23,

I never said that my code uses element wise application. To help you understand, it is basically very simple to understand, it is attempting to calculate the outer product of two vectors which results in a matrix where the (i,j)th entry is given by the product of the ith element of u and the jth element of v. For more information regarding basic concepts of array and matrixes, please refer to https://www.mathworks.com/help/matlab/learn_matlab/matrices-and-arrays.html Again, thanks for your contribution and feedback.

### Accepted Answer

Stephen23
on 15 Jul 2024

Edited: Stephen23
on 15 Jul 2024

"However, the ⊗ operator between ∇ and u isn't the simple multiplication operator *."

The Wikipedia page you linked to states "The outer product 𝑢⊗𝑣 is equivalent to a matrix multiplication 𝑢𝑣T, provided that 𝑢 is represented as a 𝑚×1 column vector and 𝑣 as a 𝑛×1 column vector (which makes 𝑣T a row vector)." So for vectors you can certainly use matrix multiplication. For higher dimension arrays you could leverage e.g. RESHAPE and TIMES ... or read the next part of my answer.

"It's the outer produt operator and hence I am finding it difficult to code it in MATLAB"

Google found this in two seconds (note: >=R2022a only):

A = rand(3,3);

B = rand(3,3);

C = tensorprod(A,B)

##### 4 Comments

Umar
on 16 Jul 2024

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