Notation of double summation
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There's a debate with some colleagues about the meaning of the notation $sum_{(i,m) neq (j,n)}$. Which one of the following is correct?
1) $sum_{(i,m) neq (j,n)} a_{i} b_{m} = sum_{i} sum_{m} a_{i} b_{m} - a_{j} b_{n}$
2) $sum_{(i,m) neq (j,n)} a_{i} b_{m} = sum_{i neq j} sum_{m neq n} a_{i} b_{m}$
I tend to say that the first one is correct since $(i,m) neq (j,n)$ should be referred to the pair and not the single indices.
summation notation
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TheDon
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There's a debate with some colleagues about the meaning of the notation $sum_{(i,m) neq (j,n)}$. Which one of the following is correct?
1) $sum_{(i,m) neq (j,n)} a_{i} b_{m} = sum_{i} sum_{m} a_{i} b_{m} - a_{j} b_{n}$
2) $sum_{(i,m) neq (j,n)} a_{i} b_{m} = sum_{i neq j} sum_{m neq n} a_{i} b_{m}$
I tend to say that the first one is correct since $(i,m) neq (j,n)$ should be referred to the pair and not the single indices.
summation notation
asked yesterday
TheDon
317313
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
There's a debate with some colleagues about the meaning of the notation $sum_{(i,m) neq (j,n)}$. Which one of the following is correct?
1) $sum_{(i,m) neq (j,n)} a_{i} b_{m} = sum_{i} sum_{m} a_{i} b_{m} - a_{j} b_{n}$
2) $sum_{(i,m) neq (j,n)} a_{i} b_{m} = sum_{i neq j} sum_{m neq n} a_{i} b_{m}$
I tend to say that the first one is correct since $(i,m) neq (j,n)$ should be referred to the pair and not the single indices.
summation notation
asked yesterday
TheDon
317313
There's a debate with some colleagues about the meaning of the notation $sum_{(i,m) neq (j,n)}$. Which one of the following is correct?
1) $sum_{(i,m) neq (j,n)} a_{i} b_{m} = sum_{i} sum_{m} a_{i} b_{m} - a_{j} b_{n}$
2) $sum_{(i,m) neq (j,n)} a_{i} b_{m} = sum_{i neq j} sum_{m neq n} a_{i} b_{m}$
I tend to say that the first one is correct since $(i,m) neq (j,n)$ should be referred to the pair and not the single indices.
summation notation
summation notation
asked yesterday
TheDon
317313
asked yesterday
TheDon
317313
asked yesterday
TheDon
317313
asked yesterday
TheDon
317313
asked yesterday
TheDon
317313
317313
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1 Answer
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The meaning of
$$sum_{(i,m)neq (j,n)} a_ib_m$$
is "the sum over all values $i,m$, except for the pair $(j,n)$." So the first sum is the correct one. Alternatively, you could write the same expression as
$$sum_{ineq j}sum_{m}a_i b_m + sum_{mneq n} a_jb_m$$
Your second expression also excludes all values of the form $(i,n)$ from the sum, which is not correct.
answered yesterday
5xum
88.7k392160
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
The meaning of
$$sum_{(i,m)neq (j,n)} a_ib_m$$
is "the sum over all values $i,m$, except for the pair $(j,n)$." So the first sum is the correct one. Alternatively, you could write the same expression as
$$sum_{ineq j}sum_{m}a_i b_m + sum_{mneq n} a_jb_m$$
Your second expression also excludes all values of the form $(i,n)$ from the sum, which is not correct.
answered yesterday
5xum
88.7k392160
add a comment |
up vote
0
down vote
accepted
The meaning of
$$sum_{(i,m)neq (j,n)} a_ib_m$$
is "the sum over all values $i,m$, except for the pair $(j,n)$." So the first sum is the correct one. Alternatively, you could write the same expression as
$$sum_{ineq j}sum_{m}a_i b_m + sum_{mneq n} a_jb_m$$
Your second expression also excludes all values of the form $(i,n)$ from the sum, which is not correct.
answered yesterday
5xum
88.7k392160
add a comment |
up vote
0
down vote
accepted
up vote
0
down vote
accepted
The meaning of
$$sum_{(i,m)neq (j,n)} a_ib_m$$
is "the sum over all values $i,m$, except for the pair $(j,n)$." So the first sum is the correct one. Alternatively, you could write the same expression as
$$sum_{ineq j}sum_{m}a_i b_m + sum_{mneq n} a_jb_m$$
Your second expression also excludes all values of the form $(i,n)$ from the sum, which is not correct.
answered yesterday
5xum
88.7k392160
The meaning of
$$sum_{(i,m)neq (j,n)} a_ib_m$$
is "the sum over all values $i,m$, except for the pair $(j,n)$." So the first sum is the correct one. Alternatively, you could write the same expression as
$$sum_{ineq j}sum_{m}a_i b_m + sum_{mneq n} a_jb_m$$
Your second expression also excludes all values of the form $(i,n)$ from the sum, which is not correct.
answered yesterday
5xum
88.7k392160
answered yesterday
5xum
88.7k392160
answered yesterday
5xum
88.7k392160
answered yesterday
5xum
88.7k392160
88.7k392160
add a comment |
add a comment |
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