# Taking outer product of two matrices

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Priyanshu le 13 Juil 2024
Commenté : Umar le 16 Juil 2024
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
⊗ = outer product of two matrices,
Can someone help me code this in MATLAB?
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Stephen23 le 15 Juil 2024
Modifié(e) : Stephen23 le 15 Juil 2024
"Hence, illustrated my example with element wise multiplication."
None of your code uses element-wise multiplication.
Umar le 15 Juil 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.

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### Réponse acceptée

Stephen23 le 15 Juil 2024
Modifié(e) : Stephen23 le 15 Juil 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)
C =
C(:,:,1,1) = 0.0016 0.0022 0.0001 0.0014 0.0007 0.0031 0.0041 0.0036 0.0037 C(:,:,2,1) = 0.0300 0.0403 0.0015 0.0265 0.0136 0.0581 0.0759 0.0680 0.0701 C(:,:,3,1) = 0.1153 0.1550 0.0059 0.1018 0.0525 0.2235 0.2921 0.2617 0.2698 C(:,:,1,2) = 0.1815 0.2438 0.0093 0.1602 0.0826 0.3515 0.4596 0.4117 0.4244 C(:,:,2,2) = 0.0327 0.0440 0.0017 0.0289 0.0149 0.0634 0.0829 0.0743 0.0766 C(:,:,3,2) = 0.1576 0.2118 0.0081 0.1392 0.0717 0.3054 0.3992 0.3576 0.3687 C(:,:,1,3) = 0.1604 0.2154 0.0082 0.1416 0.0730 0.3107 0.4061 0.3638 0.3751 C(:,:,2,3) = 0.2397 0.3220 0.0123 0.2116 0.1091 0.4643 0.6070 0.5437 0.5606 C(:,:,3,3) = 0.1568 0.2107 0.0081 0.1385 0.0714 0.3038 0.3972 0.3558 0.3669
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Priyanshu le 16 Juil 2024
Thank you for helping me with the concept. I understand the logic and i think the code will be good for me.
Umar le 16 Juil 2024
No problem Priyanshu, glad to help you out. Please let us know if you still have any further questions, all our staff people are very knowledgeable and happy to help out.

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