Help taking a cross product of a matrix

[member 428835]

hey all

well the title says it all. if i want to take the cross product of two matrices, how do i do it? any help, advice, etc. is very appreciated!

thanks

 

[CompuChip]

I don't think there's a standard definition for the cross product of two matrices. How do you think that would work, or what would it mean (e.g. the cross product of two vectors gives a vector perpendicular to both; what would the cross product of two linear transformations be)?

 

[SteamKing]

I'll take a stab: why do you want to take the cross product of two matrices, assuming such an animal exists?

 

[member 428835]

hey guys! ok, so let me explain the situation: I am in a graduate fluid mechanics course and we are dealing with tensors, which are matrices. my professor was reviewing div, del, grad, and the rest of the operators with the kronecker delta and permutation epsilon. he did mention crossing two tensors! he also mentions "dotting" or taking the dot product, of two tensors. but it seems if this is not a "thing" maybe he will elaborate in tomorrow's lecture?

thanks for both your helps! this explains why google couldn't really help me either

 

[blue_raver22]

Hello there,

To take the cross product of two matrices, you can use the following steps:

1. Make sure that the two matrices have the same number of rows and columns. If they do not have the same dimensions, the cross product cannot be computed.

2. Multiply the first matrix by the transpose of the second matrix. This will result in a new matrix with the same number of rows as the first matrix and the same number of columns as the second matrix.

3. Repeat the process, but this time multiply the second matrix by the transpose of the first matrix. This will result in a new matrix with the same number of rows as the second matrix and the same number of columns as the first matrix.

4. Subtract the two resulting matrices from each other. This will give you the cross product of the original two matrices.

I hope this helps! Let me know if you have any further questions. Good luck!