MaplePrimes - answers and comments on Question, How to write matrix inequalities (restriction for optimization)

One way

Preben Alsholm — Fri, 10 Dec 2010 11:56:14 Z

with(LinearAlgebra):
L,S:=3,4:
V:=Matrix(L,S,symbol=v);
W:=Matrix(L,S,symbol=w);
X:=Matrix(L,S,symbol=x);
Y:=Matrix(L,S,symbol=y);
seq(Transpose(V)[i].W[1..,i]<=Transpose(X)[i].Y[1..,i],i=1..S);

I have used LinearAlgebra:-Transpose to avoid the complex conjugation which is used in V[1.., i].W[1.., i]

seq

Robert Israel — Fri, 10 Dec 2010 12:07:44 Z

Compact:

seq(((V^%T . W)[i,i] <= (X^%T . Y)[i,i], i=1..S);

Of course, this is not very efficient because it calculates the same matrix product over and over again.

Somewhat better:

A:= V^%T . W; B:= X^%T . Y;
seq(A[i,i] <= B[i,i], i=1..S);

Better yet: only calculate the products you need.

with(LinearAlgebra):
seq(Column(V,i) . Column(W,i) <= Column(X,i) . Column(Y,i), i = 1 .. S);

It is enough for now

jean-jacques — Tue, 14 Dec 2010 12:05:27 Z

Thanks for the help. It is enough.

Option

hirnyk — Fri, 10 Dec 2010 12:33:49 Z

The conjugate = false option is needed in the DotProduct(Column(V, j), Column(W, j), conjugate = false) command.

thanks Robert

jean-jacques — Tue, 14 Dec 2010 12:06:28 Z

Thanks a lot for your help Robert.

Kind regards,

Jean-Jacques