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## The Matrix in Economic Geography

##### (http://faculty.washington.edu/krumme/systems/matrix.html)

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Matrix multiplications

The multiplication of matrices or vectors is "commutative", i.e. the order of the multiplicand and the multiplier cannot be reversed as is the case in regular multiplications. The process of multiplication of matrices proceeds by multiplying (more exactly: "post-multiplying") horizontal vectors by vertical vectors. The sum of the products of this multiplication of corresponding numbers of the respective vectors results in a number which is placed in the position of the resulting matrix (or vector) where the two vectors would intersect (overlap).

Thus,

 horizontal vector x vertical vector = a number -- | = x vertical vector x horizontal vector = matrix | -- =  matrix x vertical vector = vertical vector  | = | horizontal vector x matrix = horizontal vector --  = -- matrix A x matrix B = matrix C A B = C matrix B x matrix A = matrix D B A = D

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