Matrix-vector multiplication vectorization

Dear All, I have a simple 3*3 matrix(A) and large number of 3*1 vectors(v) that I want to find A*v multiplication for all of the v vectors. Instead of using "for" loop which takes so much time, how can I vectorize the matrix multiplication? Example: A=[1 2 3;4 5 6;7 8 9]; v=[1 2 3; 4 5 6; 7 8 9;10 11 12;13 14 15] (5 set of 3*1 vectors)

Answer 1

[Guillaume]

Note that v=[1 2 3; 4 5 6; 7 8 9;10 11 12;13 14 15] is 5 rows of 1x3 vectors, not 3x1 vectors.

Simply multiply your matrix by the vector matrix to get all the result vectors at once:

A=[1 2 3;4 5 6;7 8 9]; 
v=[1 2 3; 4 5 6; 7 8 9;10 11 12;13 14 15];

v = v.';  %transpose so that v is indeed 5 columns of 3x1 vectors
B = A*v   %each column of B is A*each column of v by definition of matrix multiplication

[Ivan Dubrovskiy]

it will be 3x5 matrix B?

Answer 2

[John D'Errico]

If you are storing tham in a 5x3 array, then they are 1x3 vectors, not 3x1. There is a difference.

Anyway,

A*v'

Won't work? Did you try it? If you insist on having the result be transposed again, then you could do it as:

(A*v')'

or you might recognize that this is the same as

v*A'

As long as all arrays are real. If they are complex, then becareful, as ' and .' are different operators, and you need to know which is correct.

[Shahriar]

That works. Thanks :)