Matrix Multiplication with large vectors

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amberly hadden
amberly hadden 2015-5-11
评论： Walter Roberson 2015-5-15
Hi,
If I have following problem how can I formulate it in matlab
A=
1 3
2 4
b=
xi
yi
where xi and yi are column vectors with lets say 100 values in each how can I input this problem in Matlab by using following formula
[z1 = A*b
z2]
Please note I have very large martix with vectors xi and yi and I want out put two matrices z1 and z2
Thanks in advance, jay
thanks
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amberly hadden
amberly hadden 2015-5-11
编辑：Walter Roberson 2015-5-11
Thanks walter,
So here is the thing
zi = [1 2; 3 4]*[xi;yi]
so z1 = 1*xi+2*yi
z2 = 3*xi+4*yi
coz z1 and z2 are two vectors of same size as xi and yi respectively.
Thanks very much for your guidence
Walter Roberson
Walter Roberson 2015-5-11
There seems to be some confusion about whether xi and yi are row vectors or column vectors. You said column vectors before, but [xi;yi] would create a single column vector of the two combined, with [xi,yi] producing two columns from two column vectors.

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Walter Roberson
Walter Roberson 2015-5-15
T = arrayfun(@(x,y) A*[x;y], xi, yi, 'Uniform', 0);
z1z2 = vertcat(T{:});
z1 = z1z2(:,1);
z2 = z1z2(:,2);
However, this formulation of the code would not be efficient if you had a small A and long vectors. In your actual situation, what size() is your A ?
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Walter Roberson
Walter Roberson 2015-5-15
In the case of A being 2 x 2, it is faster just to write out the values
z1 = A(1,1) * xi + A(2,1) * yi;
z2 = A(1,2) * xi + A(2,2) * yi;

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更多回答（1 个）

Thorsten
Thorsten 2015-5-12
编辑：Thorsten 2015-5-12
A = [1 2; 3 4];
xi = 10;
yi = 20;
x = [xi; yi];
z1 = A(1,:)*x;
z2 = A(2,:)*x;
or
z = A*x;
z1 = z(1);
z2 = z(2);
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amberly hadden
amberly hadden 2015-5-15
编辑：Walter Roberson 2015-5-15
Sorry I was away so could not follow up...
[z1
z2] = [1 2
3 4]*[xi
yi] xi = x1,x2,x3....x100 yi = y1,y2,y3..y100
2*2 matrix need to multiply by column vector (one in a sense but infect data has two of them) like
[a
b]

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