Is this possible? If yes, how?

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- Nov 6th 2010, 09:26 AMAniMuSVector and matrix multiplication
Is this possible? If yes, how?

Attachment 19597 - Nov 6th 2010, 09:46 AMHallsofIvy
Not as a usual matrix multiplication. In order to multiply "AB" where A and B are matrices, the number of columns of A must equal the number of rows of B. That is not true here and I do not know of any definition of "multiplcation" that will work.

You could, of course, multiply the other way:

.

Added: you could do this as a "tensor multiplication". That would involve multiplying all three elements of A by each of the 9 elements of B giving a 27 element "third order tensor". It would have to be written as a "three dimensional matrix" consisting of the three layers:

but that is probably NOT what is intended! - Nov 6th 2010, 10:05 AMAniMuS
This is more about vector multiplication it seems, i thought it should be similar (sorry if i misled you). My teacher wrote this at the time, and i didn't get it. I know we can't multiply two matrices if the 1st doesn't have the same number of columns as the 2nd has of rows. So as he did it, then i suppose matrices rules don't apply here. Probably there is some other rule to multiply these two vectors...

Forget the initial vector and matrix multiplication, this one reflects better my doubt.

. - Nov 6th 2010, 10:24 AMHallsofIvy
Oh! That's the "cross product" of two three dimensional vectors. Given two vectors, and , then the cross product is given by . That can be remember by a mnemonic: write it as a "determinant":

Now, cross-multiplication is "anti-symmetric": and, in fact, what you have is the other way around:

while

The cross product cannot be generalized in any simple way to a product of a vector with a matrix or even to other dimensions. The cross product of two two-dimensional vectors is taken by treating them as three dimensional vectors with third component 0.