Quick questions about summation notation used in my book
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My Questions
In the screenshot below, is the summation notation in the orange (top) box and blue (bottom) box the exact same? So in a 3 by 3 matrix you'd only want to sum $a_12+a_13+a_23$
Is it correct to say that the orange box is exactly the same as
$$sum_i=1^n-1 sum_j=i+1^n P(A_i A_j)$$
- Is it correct to say that the BLUE box is exactly the same as
$$sum_(i,j):i<j E[min(X_i,X_j)]$$
Why would you choose one notation or the other? It seems the blue box is faster to write
Is it correct to say that the following will always hold if $i$ and $j$ span the exact same indices and $a_ij = a_ji$ for all $i$ and $j$?
$$sum_i neq j a_ij = 2sum_i<j a_ij$$
Thank you for your time and patience.
algebra-precalculus
asked Aug 26 at 19:51
HJ_beginner
608115
add a comment |Â
up vote
2
down vote
favorite
My Questions
In the screenshot below, is the summation notation in the orange (top) box and blue (bottom) box the exact same? So in a 3 by 3 matrix you'd only want to sum $a_12+a_13+a_23$
Is it correct to say that the orange box is exactly the same as
$$sum_i=1^n-1 sum_j=i+1^n P(A_i A_j)$$
- Is it correct to say that the BLUE box is exactly the same as
$$sum_(i,j):i<j E[min(X_i,X_j)]$$
Why would you choose one notation or the other? It seems the blue box is faster to write
Is it correct to say that the following will always hold if $i$ and $j$ span the exact same indices and $a_ij = a_ji$ for all $i$ and $j$?
$$sum_i neq j a_ij = 2sum_i<j a_ij$$
Thank you for your time and patience.
algebra-precalculus
asked Aug 26 at 19:51
HJ_beginner
608115
1
for 1. , 2. , 3. , 5. I would just say "you are correct". Talking about 4. , I don't think there is a preferable one, everything is ok until it is clear enough.
– LucaMac
Aug 26 at 19:59
@LucaMac Thanks for your confirmation, since this summation notation shows up everywhere I want to make sure I have an exact understanding or it makes me feel uneasy when trying to learn new concepts. I wonder why the author of my book (who I admire quite a bit) jumps around with the notation... but I suppose you're right it just has to be clear enough
– HJ_beginner
Aug 26 at 20:03
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
My Questions
In the screenshot below, is the summation notation in the orange (top) box and blue (bottom) box the exact same? So in a 3 by 3 matrix you'd only want to sum $a_12+a_13+a_23$
Is it correct to say that the orange box is exactly the same as
$$sum_i=1^n-1 sum_j=i+1^n P(A_i A_j)$$
- Is it correct to say that the BLUE box is exactly the same as
$$sum_(i,j):i<j E[min(X_i,X_j)]$$
Why would you choose one notation or the other? It seems the blue box is faster to write
Is it correct to say that the following will always hold if $i$ and $j$ span the exact same indices and $a_ij = a_ji$ for all $i$ and $j$?
$$sum_i neq j a_ij = 2sum_i<j a_ij$$
Thank you for your time and patience.
algebra-precalculus
asked Aug 26 at 19:51
HJ_beginner
608115
My Questions
In the screenshot below, is the summation notation in the orange (top) box and blue (bottom) box the exact same? So in a 3 by 3 matrix you'd only want to sum $a_12+a_13+a_23$
Is it correct to say that the orange box is exactly the same as
$$sum_i=1^n-1 sum_j=i+1^n P(A_i A_j)$$
- Is it correct to say that the BLUE box is exactly the same as
$$sum_(i,j):i<j E[min(X_i,X_j)]$$
Why would you choose one notation or the other? It seems the blue box is faster to write
Is it correct to say that the following will always hold if $i$ and $j$ span the exact same indices and $a_ij = a_ji$ for all $i$ and $j$?
$$sum_i neq j a_ij = 2sum_i<j a_ij$$
Thank you for your time and patience.
algebra-precalculus
asked Aug 26 at 19:51
HJ_beginner
608115
asked Aug 26 at 19:51
HJ_beginner
608115
asked Aug 26 at 19:51
HJ_beginner
608115
asked Aug 26 at 19:51
HJ_beginner
608115
608115
1
for 1. , 2. , 3. , 5. I would just say "you are correct". Talking about 4. , I don't think there is a preferable one, everything is ok until it is clear enough.
– LucaMac
Aug 26 at 19:59
@LucaMac Thanks for your confirmation, since this summation notation shows up everywhere I want to make sure I have an exact understanding or it makes me feel uneasy when trying to learn new concepts. I wonder why the author of my book (who I admire quite a bit) jumps around with the notation... but I suppose you're right it just has to be clear enough
– HJ_beginner
Aug 26 at 20:03
add a comment |Â
1
for 1. , 2. , 3. , 5. I would just say "you are correct". Talking about 4. , I don't think there is a preferable one, everything is ok until it is clear enough.
– LucaMac
Aug 26 at 19:59
@LucaMac Thanks for your confirmation, since this summation notation shows up everywhere I want to make sure I have an exact understanding or it makes me feel uneasy when trying to learn new concepts. I wonder why the author of my book (who I admire quite a bit) jumps around with the notation... but I suppose you're right it just has to be clear enough
– HJ_beginner
Aug 26 at 20:03
1
1
for 1. , 2. , 3. , 5. I would just say "you are correct". Talking about 4. , I don't think there is a preferable one, everything is ok until it is clear enough.
– LucaMac
Aug 26 at 19:59
for 1. , 2. , 3. , 5. I would just say "you are correct". Talking about 4. , I don't think there is a preferable one, everything is ok until it is clear enough.
– LucaMac
Aug 26 at 19:59
@LucaMac Thanks for your confirmation, since this summation notation shows up everywhere I want to make sure I have an exact understanding or it makes me feel uneasy when trying to learn new concepts. I wonder why the author of my book (who I admire quite a bit) jumps around with the notation... but I suppose you're right it just has to be clear enough
– HJ_beginner
Aug 26 at 20:03
@LucaMac Thanks for your confirmation, since this summation notation shows up everywhere I want to make sure I have an exact understanding or it makes me feel uneasy when trying to learn new concepts. I wonder why the author of my book (who I admire quite a bit) jumps around with the notation... but I suppose you're right it just has to be clear enough
– HJ_beginner
Aug 26 at 20:03
add a comment |Â
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1
for 1. , 2. , 3. , 5. I would just say "you are correct". Talking about 4. , I don't think there is a preferable one, everything is ok until it is clear enough.
– LucaMac
Aug 26 at 19:59
@LucaMac Thanks for your confirmation, since this summation notation shows up everywhere I want to make sure I have an exact understanding or it makes me feel uneasy when trying to learn new concepts. I wonder why the author of my book (who I admire quite a bit) jumps around with the notation... but I suppose you're right it just has to be clear enough
– HJ_beginner
Aug 26 at 20:03