How do I vector product by matrix and between matrices?

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How do I vector product by matrix and between matrices?

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#1 by (2 votes)

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I can not think of a for doing this multiplication, because the number of columns of the first array has to be equal to the number of rows of the second array ...

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asked by anonymous 16.10.2017 / 00:45

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Dot Matrix

Before making any code you need to know how the product works between arrays.

Considering two matrices A and B the matrix product is done by multiplying each value of a line of A by each value of a column of B and adding them all partials. This process is thus applied to each line of A and column B .

See an illustration of this process:

ConsideringarraysoftheAillustrationwithdimension4x2andB2x3,theresultingarray,whichI'llcallR,willhavethe4x3size.Hereyouseethattheresultingarraymusthavethenumberofrowsofthefirstarrayandthenumberofcolumnsofthesecondarray.

InthisarrayRthefirsthouseR11wouldthenbedefinedby:

R11=A11*B11+A12*B21;

ThesecondhouseR12,whichishighlightedinthefigurewouldbecalculatedas:

R12=A11*B12+A12*B22;

Andthesameprocessappliestotheend.

CalculationinC

Nowthatweknowhowtheproductworksbetweenarrays,wecanmoveontoimplementation.Youhaveindicatedaforforsolvingtheproblemandinfactyouwillneed3forthis.Thefirst2forcyclesthrougheachcelloftheresultingarrayand3cyclesthroughAandBtodothecalculation.

intA[2][2]={{1,2},{3,4}};intB[2][2]={{2,0},{1,2}};intR[2][2]={0};inti,j,k;for(i=0;i<2;i++){for(j=0;j<2;j++){for(k=0;k<2;k++){R[i][j]+=A[i][k]*B[k][j];}}}

See the Ideone example

Note: The product between vector and array is the same thing as the product between array and array, since a vector is a particular case of a matrix with only one row or column.