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vector into matrix


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#1 AlexRus   Members   -  Reputation: 195

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Posted 16 March 2014 - 06:35 PM

Hello, i am a little bit stuck with a formula that i need to figure out and code.

 

Picture is attached.
Original source http://www.beosil.com/download/MeshlessDeformations_SIG05.pdf

 

Apq = matrix(3x3)

m = is mass(float)

 

p = is position vector(x,y,z)

q = is transpose of position vector.

 

i need to calculate Apq.

what confuses me a little bit is that the output should be a matrix.

 

how should this matrix be assembled? as far as i know multiplication of vectors(p and q) will give me a float number , and not a matrix;

 

Thanks!

Attached Thumbnails

  • multi.jpg

Edited by AlexRus, 16 March 2014 - 06:36 PM.


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#2 Bacterius   Crossbones+   -  Reputation: 9293

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Posted 16 March 2014 - 06:46 PM

Do you know the outer product? The dot product is the inner product, which multiplies a 1*n matrix (row vector) with an n*1 matrix (column vector) and gives a 1*1 matrix (a scalar). The outer product multiplies a n*1 matrix with an 1*n matrix to obtain an n*n matrix. This is what you want here: p and q are column vectors (3*1) and their transpose is a row vector (1*3). Multiplying them together gives you a 3*3 matrix. You use the same rules as ordinary matrix multiplication to compute this outer product.

 

Reading: http://en.wikipedia.org/wiki/Outer_product


The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.

 

- Pessimal Algorithms and Simplexity Analysis





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