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Wednesday, February 08, 2006 

Compare, Contrast.

One similarity that I can think of at the moment for scalar multiplication, matrix multiplication, and normal multiplication is that you may multiply them in any order and the product will be the same, for matrix multiplication this is if the matricies in question are the same. I believe that's how it is in the case of matrix multiplication, anyway. :P I'm confusing myself trying to explain this. :P

The differences between the three is that while it doesn't matter with scalar multiplication and normal multiplication in any case, when matricies are not the same, if placed in a different order, the product will be different. Another difference is that with matrix multiplication, there's the funky process where it's A11 x B11 + A12 x B21 ... A being the first Matrix and B being the second. 11 being the first row and first column, 12 being the first row and second column, and 21 being the second row and first column. Then you do A11 x B12 + A12 x B22, etc, etc, etc.

That's all my head will allow me to produce without it imploding, I hope I've got it right.

As for the two 2 by 2's that produce the same resultant matrix:

Matrix A = 33 55 Matrix B = 33 55 Matrix C = 2424 4040
Matrix A = 12 21 Matrix B = 12 21 Matrix C = 54 45

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Wait, I think I explained the matrix multiplication wrong.. Ah well.

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