Matrix Multiplication with large vectors

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

[Walter Roberson]

Is the number of rows in A the same as the number of elements in xi and yi?

Are you looking for

z1 = A(:,1) .* xi;
z2 = A(:,2) .* yi;

?

[amberly hadden]

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]

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.

Answer 1

[Walter Roberson]

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 ?

[amberly hadden]

thanks, Walter apreciated

[Walter Roberson]

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;

Answer 2

[Thorsten]

 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);

[amberly hadden]

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]