How Do L and U Sums Differ in Double Summation?

[dbatten]

Homework Statement

Consider any sequence a₁, a₂,..., a_n and the nxn array of values b_ij = a_ia_j. Which terms in the array are involved in the sums L = Ʃ(between i=1 and n)Ʃ(between j=1 and i) b_ij
and U = Ʃ(between j=1 and n)Ʃ(between i=1 and j) b_ij?

Also, by symmetry, show that L=U.

Homework Equations

n/a

The Attempt at a Solution

I've just started this topic and the double summation is really confusing me. Any guidance or suggestions on how to approach this would be really useful thanks.

 

[SammyS]

Homework Statement

Consider any sequence a₁, a₂,..., a_n and the nxn array of values b_ij = a_ia_j. Which terms in the array are involved in the sums L = Ʃ(between i=1 and n)Ʃ(between j=1 and i) b_ij
and U = Ʃ(between j=1 and n)Ʃ(between i=1 and j) b_ij?

Also, by symmetry, show that L=U.

Homework Equations

The Attempt at a Solution

I've just started this topic and the double summation is really confusing me. Any guidance or suggestions on how to approach this would be really useful thanks.

Just do a small example by hand. Use maybe a 5 by 5 array of b_i,j .

a₁a₁ a₁a₂ a₁a₃ a₁a₄ a₁a₅ 

a₂a₁ a₂a₂ a₂a₃ a₂a₄ a₂a₅

a₃a₁ a₃a₂ a₃a₃ a₃a₄ a₃a₅

a₄a₁ a₄a₂ a₄a₃ a₄a₄ a₄a₅

a₅a₁ a₅a₂ a₅a₃ a₅a₄ a₅a₅