dot product between system of vectors

Question

bidlee devi 2020-1-26

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https://ww2.mathworks.cn/matlabcentral/answers/502014-dot-product-between-system-of-vectors

评论： Turlough Hughes 2020-1-26

Suppose we have a system of vectors Z and Y of size 3 *3 consisitng of three column vectors with three tuples in each colunm.

Z=[45 33 37 ; 39 28 37 ;35 36 48 ]

Y=[ 29.5 30 30 ;29.51 30 30 ;29.51 30 29 ]

How to write a matlab code to get Q of size 3*3 given by

Q=[10000.88925 9410.822 10295.99 ;10001.81888 9411.39 10296.72 ;10000.49116 9410.226 10295.24 ]

Here, in Q , element in (1,1) is a dot product between first column of Z and first column of Y. Likewise element in (2,1) is a dot product of second column of Y and first column of Z so on element (3,1) is a dot product between first column of Z and third column of Y. In this way, the first column of Q is formed. Moreover, for example, element (2,3) is a dot product between second column of Y and third column of Z and so forth

Can anyone help me out on how to automate this using matlab codes ? urgently needed.

Thanks in advance.

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Stephen23 2020-1-26

编辑：Stephen23 2020-1-26

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Your example output values appear to be incorrect:

>> Y.'*Z
ans =
   3511.2   2862.1   3599.8
   3570.0   2910.0   3660.0
   3535.0   2874.0   3612.0

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Answer 1

Thiago Henrique Gomes Lobato 2020-1-26

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https://ww2.mathworks.cn/matlabcentral/answers/502014-dot-product-between-system-of-vectors#answer_412065

在 MATLAB Online 中打开

How you are getting these values for Q? If you calculate the dot product between the colums of the variables you give the values are different, maybe you had a small error on your code? Back to your question this is basically a transpose matrix multiplication. A normal matrix multiplication is basically the dot product between rows and columns, if you transpose the first matrix you get the dot product of columns and columns, as you want. As example:

 Z=[45  33  37    ;  39  28  37  ;35  36  48  ];
 Y=[ 29.5  30  30  ;29.51  30  30 ;29.51  30  29   ];
 
 A1 = zeros(3);
 % Loop to do column dot product
 for idxX = 1:3
     for idxY = 1:3
 A1(idxX,idxY) = dot(Z(:,idxX),Y(:,idxY));
     end
 end
 A2 =  Z'*Y; % Transpose matrix multiplication
 
 A1
 A2
 norm(A1-A2)
 
 A1 =
   1.0e+03 *
    3.5112    3.5700    3.5350
    2.8621    2.9100    2.8740
    3.5999    3.6600    3.6120
A2 =
   1.0e+03 *
    3.5112    3.5700    3.5350
    2.8621    2.9100    2.8740
    3.5998    3.6600    3.6120
ans =
   6.4311e-13