graph theory and linear algebra
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
add a comment |
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
Can you post the entire exact question?
– The Count
Nov 19 '18 at 1:40
The charactersanddon't render properly on my computer. What are they supposed to be?
– Omnomnomnom
Nov 20 '18 at 3:51
add a comment |
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
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
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 charactersanddon't render properly on my computer. What are they supposed to be?
– Omnomnomnom
Nov 20 '18 at 3:51
add a comment |
Can you post the entire exact question?
– The Count
Nov 19 '18 at 1:40
The charactersanddon'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
add a comment |
1 Answer
1
active
oldest
votes
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.
answered Nov 20 '18 at 3:59
Omnomnomnom
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
add a comment |
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
answered Nov 20 '18 at 3:59
Omnomnomnom
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
add a comment |
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.
answered Nov 20 '18 at 3:59
Omnomnomnom
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
add a comment |
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.
answered Nov 20 '18 at 3:59
Omnomnomnom
126k788176
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.
answered Nov 20 '18 at 3:59
Omnomnomnom
126k788176
answered Nov 20 '18 at 3:59
Omnomnomnom
126k788176
answered Nov 20 '18 at 3:59
Omnomnomnom
126k788176
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
add a comment |
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
add a comment |
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Can you post the entire exact question?
– The Count
Nov 19 '18 at 1:40
The characters
anddon't render properly on my computer. What are they supposed to be?– Omnomnomnom
Nov 20 '18 at 3:51