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A question about the cross product as related to matrix multiplication 
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#1
Feb2814, 09:35 PM

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I understand that the cross product, in lay mans terms doesn't exist unless we're in 3 dimensions.
When you multiply two matrices together I have been told you get something similar. I hear that this is because a matrix can be treated as a vector. So if we are talking about measurable things, in the real world does matrix multiplication have any relevance ? I might be off the mark but what if we were to build a model, based on height weight and income would that be definable in 3 dimensions and therefore if you had two sets of observation and you multiplied them the answer would be nonsense but somehow it has a definition in 3 dimensions as a new matrix ? if for example, i had a range of multiplies I wanted to apply to each observation or set of observations, stored in a matrix then this would be a scalar multiplication of a matrix onto another matrix ? Does such a thing exist. Apologies I am not a mathematician so my terminology is buggered but I'm still curious. Thanks, 


#2
Feb2814, 11:23 PM

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Matrix multiplication is used all the time to design structures, calculate stresses, etc. It's a tool which makes doing certain mathematical calculations easier to organize and handle, especially for computers. It's like asking if regular multiplication has any relevance.



#3
Feb2814, 11:39 PM

P: 163

Do you have some examples ? Because when I looked at some examples for vector cross product it started to make some sense. Especially when they said it only exists in 3 dimensions. 


#4
Mar114, 12:04 AM

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A question about the cross product as related to matrix multiplication
The cross product as defined for cartesian coordinates exists and has meaning for 3 dimensions and 7 dimensions.
http://en.wikipedia.org/wiki/Cross_product The reasons for this are quite mathematically abstract. The simplest application for matrix multiplication would probably be solving a system of simultaneous linear equations. I can't give you anything simpler than that, just like you would be hard pressed to explain multiplication to a first grader who is just learning to add. Simple matrix manipulations are usually first discussed in algebra classes in middle or high school. http://www.mathwarehouse.com/algebra...plymatrix.php Simultaneous linear equations: http://en.wikipedia.org/wiki/System_of_linear_equations 


#5
Mar114, 12:19 AM

P: 163

For a system a linear equations it doesn't make sense, because you're multiplying a row by a column. 


#6
Mar114, 12:29 AM

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$$\begin{bmatrix} x_1 & x_2 & ... & x_n\end{bmatrix} \begin{bmatrix}y_1 \\ y_2 \\ ... \\ y_n \end{bmatrix}$$ $$=x_1y_1 + x_2y_2 + ... + x_ny_n$$ 


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Mar114, 01:18 AM

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#8
Mar114, 01:39 AM

P: 163




#9
Mar114, 11:51 AM

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Matrix multiplication involves one dot product for each element in the product matrix. Matrix multiplication doesn't have anything to do with the cross product.



#10
Mar114, 12:43 PM

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