Let's say further, that you want to represent the double summation, equivalent to the following two for loops, without using loops, since Octave and Matlab suck at loops.
DoubleSum = 0;
for i = 1:n
for j = 1:N
DoubleSum += t(i) * T(j);
Here's one possible method, using the intrinsic function sum.
DoubleSum = sum(sum((t * T')))
If you know some Octave, you will be able to parse the command by yourself.
Let's throw in another wrinkle. Let's say, that in addition to t and T, we had another N*1 vector g, and we wanted to find the double summation corresponding to the quantity g(j)*exp(-t(i)/T(j)), instead of t(i)*T(j) in the double for loop above.
DoubleSum = sum(exp(-t * (1./T)') * g)