graph theory and linear algebra












-1














I have a flow graph that gives me the flow matrix below. How do I compute $Aodot A$ and $A odot A odot A$? I'm not familiar with this operator and can't really find anything about it. The hint that was given is that "Given $A = [a_{ij}]$ and $B = [b_{kl}]$ of size $n × m$ and $m × l$ respectively, we define
$A odot B= [max_{1leq k leq m} min(a_{ik},b_{kl})]$."



MY WORK
The flow graph I get gives me the flow matrix
begin{array}{ccccc}
0 & 0 & 2 & 0 & 0 \
3 & 0 & 8 & 1 & 0 \
0 & 0 & 0 & 0 & 7 \
2 & 0 & 0 & 0 & 4 \
0 & 0 & 10 & 0 & 4 \
end{array}



NOV 19
Using the method below I got



$Aodot A= begin{array}{ccccc}
0 & 0 & 0 & 0 & 2 \
1 & 0 & 2 & 0 & 7 \
0 & 0 & 7 & 0 & 4 \
0 & 0 & 4 & 0 & 4 \
0 & 0 & 4 & 0 & 7 \
end{array}$



$Aodot Aodot A= begin{array}{ccccc}
0 & 0 & 2 & 0 & 2 \
0 & 0 & 7 & 0 & 4 \
0 & 0 & 4 & 0 & 7 \
0 & 0 & 4 & 0 & 4 \
0 & 0 & 7 & 0 & 4 \
end{array}$



Did I make a mistake or are these correct?






combinatorics matrices discrete-mathematics graph-theory







share|cite|improve this question
























  • Can you post the entire exact question?
    – The Count
    Nov 19 '18 at 1:40










  • The characters 􏰄 and 􏰅 don't render properly on my computer. What are they supposed to be?
    – Omnomnomnom
    Nov 20 '18 at 3:51
















-1














I have a flow graph that gives me the flow matrix below. How do I compute $Aodot A$ and $A odot A odot A$? I'm not familiar with this operator and can't really find anything about it. The hint that was given is that "Given $A = [a_{ij}]$ and $B = [b_{kl}]$ of size $n × m$ and $m × l$ respectively, we define
$A odot B= [max_{1leq k leq m} min(a_{ik},b_{kl})]$."



MY WORK
The flow graph I get gives me the flow matrix
begin{array}{ccccc}
0 & 0 & 2 & 0 & 0 \
3 & 0 & 8 & 1 & 0 \
0 & 0 & 0 & 0 & 7 \
2 & 0 & 0 & 0 & 4 \
0 & 0 & 10 & 0 & 4 \
end{array}



NOV 19
Using the method below I got



$Aodot A= begin{array}{ccccc}
0 & 0 & 0 & 0 & 2 \
1 & 0 & 2 & 0 & 7 \
0 & 0 & 7 & 0 & 4 \
0 & 0 & 4 & 0 & 4 \
0 & 0 & 4 & 0 & 7 \
end{array}$



$Aodot Aodot A= begin{array}{ccccc}
0 & 0 & 2 & 0 & 2 \
0 & 0 & 7 & 0 & 4 \
0 & 0 & 4 & 0 & 7 \
0 & 0 & 4 & 0 & 4 \
0 & 0 & 7 & 0 & 4 \
end{array}$



Did I make a mistake or are these correct?






combinatorics matrices discrete-mathematics graph-theory







share|cite|improve this question
























  • Can you post the entire exact question?
    – The Count
    Nov 19 '18 at 1:40










  • The characters 􏰄 and 􏰅 don't render properly on my computer. What are they supposed to be?
    – Omnomnomnom
    Nov 20 '18 at 3:51














-1












-1








-1







I have a flow graph that gives me the flow matrix below. How do I compute $Aodot A$ and $A odot A odot A$? I'm not familiar with this operator and can't really find anything about it. The hint that was given is that "Given $A = [a_{ij}]$ and $B = [b_{kl}]$ of size $n × m$ and $m × l$ respectively, we define
$A odot B= [max_{1leq k leq m} min(a_{ik},b_{kl})]$."



MY WORK
The flow graph I get gives me the flow matrix
begin{array}{ccccc}
0 & 0 & 2 & 0 & 0 \
3 & 0 & 8 & 1 & 0 \
0 & 0 & 0 & 0 & 7 \
2 & 0 & 0 & 0 & 4 \
0 & 0 & 10 & 0 & 4 \
end{array}



NOV 19
Using the method below I got



$Aodot A= begin{array}{ccccc}
0 & 0 & 0 & 0 & 2 \
1 & 0 & 2 & 0 & 7 \
0 & 0 & 7 & 0 & 4 \
0 & 0 & 4 & 0 & 4 \
0 & 0 & 4 & 0 & 7 \
end{array}$



$Aodot Aodot A= begin{array}{ccccc}
0 & 0 & 2 & 0 & 2 \
0 & 0 & 7 & 0 & 4 \
0 & 0 & 4 & 0 & 7 \
0 & 0 & 4 & 0 & 4 \
0 & 0 & 7 & 0 & 4 \
end{array}$



Did I make a mistake or are these correct?






combinatorics matrices discrete-mathematics graph-theory







share|cite|improve this question















I have a flow graph that gives me the flow matrix below. How do I compute $Aodot A$ and $A odot A odot A$? I'm not familiar with this operator and can't really find anything about it. The hint that was given is that "Given $A = [a_{ij}]$ and $B = [b_{kl}]$ of size $n × m$ and $m × l$ respectively, we define
$A odot B= [max_{1leq k leq m} min(a_{ik},b_{kl})]$."



MY WORK
The flow graph I get gives me the flow matrix
begin{array}{ccccc}
0 & 0 & 2 & 0 & 0 \
3 & 0 & 8 & 1 & 0 \
0 & 0 & 0 & 0 & 7 \
2 & 0 & 0 & 0 & 4 \
0 & 0 & 10 & 0 & 4 \
end{array}



NOV 19
Using the method below I got



$Aodot A= begin{array}{ccccc}
0 & 0 & 0 & 0 & 2 \
1 & 0 & 2 & 0 & 7 \
0 & 0 & 7 & 0 & 4 \
0 & 0 & 4 & 0 & 4 \
0 & 0 & 4 & 0 & 7 \
end{array}$



$Aodot Aodot A= begin{array}{ccccc}
0 & 0 & 2 & 0 & 2 \
0 & 0 & 7 & 0 & 4 \
0 & 0 & 4 & 0 & 7 \
0 & 0 & 4 & 0 & 4 \
0 & 0 & 7 & 0 & 4 \
end{array}$



Did I make a mistake or are these correct?






combinatorics matrices discrete-mathematics graph-theory




combinatorics matrices discrete-mathematics graph-theory






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 21 '18 at 22:37

























asked Nov 19 '18 at 1:35







user497933



















  • Can you post the entire exact question?
    – The Count
    Nov 19 '18 at 1:40










  • The characters 􏰄 and 􏰅 don't render properly on my computer. What are they supposed to be?
    – Omnomnomnom
    Nov 20 '18 at 3:51


















  • Can you post the entire exact question?
    – The Count
    Nov 19 '18 at 1:40










  • The characters 􏰄 and 􏰅 don't render properly on my computer. What are they supposed to be?
    – Omnomnomnom
    Nov 20 '18 at 3:51
















Can you post the entire exact question?
– The Count
Nov 19 '18 at 1:40




Can you post the entire exact question?
– The Count
Nov 19 '18 at 1:40












The characters 􏰄 and 􏰅 don't render properly on my computer. What are they supposed to be?
– Omnomnomnom
Nov 20 '18 at 3:51




The characters 􏰄 and 􏰅 don't render properly on my computer. What are they supposed to be?
– Omnomnomnom
Nov 20 '18 at 3:51










1 Answer
1






active

oldest

votes


















0














The definition $[A⊙B]_{il}= [max_{1≤k≤m} min(a_{ik},b_{kl})]$ is enough for us to compute the desired matrices. For example: for $A odot A$, we compute
$$
[Aodot A]_{23} = max_{1 leq k leq 5} min(a_{2k}, a_{k3})\
= max{min(3,2),min(0,8),min(8,0),min(1,0), min(0,10)} \
= max{2,0,0,0,0)} = 2
$$
Which is to say that
$$
A odot A = pmatrix{?&?&?&?&?\
?&?&color{red}2&?&?\
?&?&?&?&?\
?&?&?&?&?\
?&?&?&?&?\}
$$
The computation of the remaining entries is similar.






share|cite|improve this answer





















  • For A⊙A⊙A, im assuming it would be similar except instead of 2 "leaps" it would be 3?
    – user497933
    Nov 20 '18 at 4:20











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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









0














The definition $[A⊙B]_{il}= [max_{1≤k≤m} min(a_{ik},b_{kl})]$ is enough for us to compute the desired matrices. For example: for $A odot A$, we compute
$$
[Aodot A]_{23} = max_{1 leq k leq 5} min(a_{2k}, a_{k3})\
= max{min(3,2),min(0,8),min(8,0),min(1,0), min(0,10)} \
= max{2,0,0,0,0)} = 2
$$
Which is to say that
$$
A odot A = pmatrix{?&?&?&?&?\
?&?&color{red}2&?&?\
?&?&?&?&?\
?&?&?&?&?\
?&?&?&?&?\}
$$
The computation of the remaining entries is similar.






share|cite|improve this answer





















  • For A⊙A⊙A, im assuming it would be similar except instead of 2 "leaps" it would be 3?
    – user497933
    Nov 20 '18 at 4:20
















0














The definition $[A⊙B]_{il}= [max_{1≤k≤m} min(a_{ik},b_{kl})]$ is enough for us to compute the desired matrices. For example: for $A odot A$, we compute
$$
[Aodot A]_{23} = max_{1 leq k leq 5} min(a_{2k}, a_{k3})\
= max{min(3,2),min(0,8),min(8,0),min(1,0), min(0,10)} \
= max{2,0,0,0,0)} = 2
$$
Which is to say that
$$
A odot A = pmatrix{?&?&?&?&?\
?&?&color{red}2&?&?\
?&?&?&?&?\
?&?&?&?&?\
?&?&?&?&?\}
$$
The computation of the remaining entries is similar.






share|cite|improve this answer





















  • For A⊙A⊙A, im assuming it would be similar except instead of 2 "leaps" it would be 3?
    – user497933
    Nov 20 '18 at 4:20














0












0








0






The definition $[A⊙B]_{il}= [max_{1≤k≤m} min(a_{ik},b_{kl})]$ is enough for us to compute the desired matrices. For example: for $A odot A$, we compute
$$
[Aodot A]_{23} = max_{1 leq k leq 5} min(a_{2k}, a_{k3})\
= max{min(3,2),min(0,8),min(8,0),min(1,0), min(0,10)} \
= max{2,0,0,0,0)} = 2
$$
Which is to say that
$$
A odot A = pmatrix{?&?&?&?&?\
?&?&color{red}2&?&?\
?&?&?&?&?\
?&?&?&?&?\
?&?&?&?&?\}
$$
The computation of the remaining entries is similar.






share|cite|improve this answer












The definition $[A⊙B]_{il}= [max_{1≤k≤m} min(a_{ik},b_{kl})]$ is enough for us to compute the desired matrices. For example: for $A odot A$, we compute
$$
[Aodot A]_{23} = max_{1 leq k leq 5} min(a_{2k}, a_{k3})\
= max{min(3,2),min(0,8),min(8,0),min(1,0), min(0,10)} \
= max{2,0,0,0,0)} = 2
$$
Which is to say that
$$
A odot A = pmatrix{?&?&?&?&?\
?&?&color{red}2&?&?\
?&?&?&?&?\
?&?&?&?&?\
?&?&?&?&?\}
$$
The computation of the remaining entries is similar.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Nov 20 '18 at 3:59









Omnomnomnom

126k788176




126k788176












  • For A⊙A⊙A, im assuming it would be similar except instead of 2 "leaps" it would be 3?
    – user497933
    Nov 20 '18 at 4:20


















  • For A⊙A⊙A, im assuming it would be similar except instead of 2 "leaps" it would be 3?
    – user497933
    Nov 20 '18 at 4:20
















For A⊙A⊙A, im assuming it would be similar except instead of 2 "leaps" it would be 3?
– user497933
Nov 20 '18 at 4:20




For A⊙A⊙A, im assuming it would be similar except instead of 2 "leaps" it would be 3?
– user497933
Nov 20 '18 at 4:20


















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