Is $sumlimits_k fracW_ik H_kjsumlimits_k W_ik H_kj$ = 1?
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I derive an equation and get the term $sumlimits_k fracW_ik H_kjsumlimits_k W_ik H_kj$. I think this term is equal to 1 because
Proof:
$sumlimits_k fracW_ik H_kj(sumlimits_k W_ik H_kj)_ij = frac1(sumlimits_k W_ik H_kj)_ij times sumlimits_k W_ik H_kj = 1$
where $W$ and $H$ are matrices with dimension $i times k$ and $k times j$, respectively
I just wonder is this proof correct?
matrices proof-verification matrix-equations
 |Â
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up vote
0
down vote
favorite
I derive an equation and get the term $sumlimits_k fracW_ik H_kjsumlimits_k W_ik H_kj$. I think this term is equal to 1 because
Proof:
$sumlimits_k fracW_ik H_kj(sumlimits_k W_ik H_kj)_ij = frac1(sumlimits_k W_ik H_kj)_ij times sumlimits_k W_ik H_kj = 1$
where $W$ and $H$ are matrices with dimension $i times k$ and $k times j$, respectively
I just wonder is this proof correct?
matrices proof-verification matrix-equations
3
Your notations are horrendous. First, what is $(Sigma_k W_ik H_kj)_ij$? Second, why do you use the same index in the outer sum and in the inner sum? Third, the symbol for sums issum
, notSigma
. What is right however is that $$sum_k fracW_ik H_kjsumlimits_ell W_iell H_ell j=frac1sumlimits_ell W_iell H_ell jsum_k W_ik H_kj=1$$
â Did
Sep 5 at 5:49
@Did: Looks like an answer to me?
â joriki
Sep 5 at 5:56
@joriki Free to use, anyway.
â Did
Sep 5 at 5:59
@Did if you may answer below, I would accept it. Sorry forsum
andSigma
. I used the same index because they are the same matrix. But I think I get your point.
â Jan
Sep 5 at 6:01
This "mess of indices" is already seen here. It is the source of problems.
â metamorphy
Sep 5 at 7:01
 |Â
show 1 more comment
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I derive an equation and get the term $sumlimits_k fracW_ik H_kjsumlimits_k W_ik H_kj$. I think this term is equal to 1 because
Proof:
$sumlimits_k fracW_ik H_kj(sumlimits_k W_ik H_kj)_ij = frac1(sumlimits_k W_ik H_kj)_ij times sumlimits_k W_ik H_kj = 1$
where $W$ and $H$ are matrices with dimension $i times k$ and $k times j$, respectively
I just wonder is this proof correct?
matrices proof-verification matrix-equations
I derive an equation and get the term $sumlimits_k fracW_ik H_kjsumlimits_k W_ik H_kj$. I think this term is equal to 1 because
Proof:
$sumlimits_k fracW_ik H_kj(sumlimits_k W_ik H_kj)_ij = frac1(sumlimits_k W_ik H_kj)_ij times sumlimits_k W_ik H_kj = 1$
where $W$ and $H$ are matrices with dimension $i times k$ and $k times j$, respectively
I just wonder is this proof correct?
matrices proof-verification matrix-equations
matrices proof-verification matrix-equations
edited Sep 10 at 20:19
Did
243k23209445
243k23209445
asked Sep 5 at 5:40
Jan
1747
1747
3
Your notations are horrendous. First, what is $(Sigma_k W_ik H_kj)_ij$? Second, why do you use the same index in the outer sum and in the inner sum? Third, the symbol for sums issum
, notSigma
. What is right however is that $$sum_k fracW_ik H_kjsumlimits_ell W_iell H_ell j=frac1sumlimits_ell W_iell H_ell jsum_k W_ik H_kj=1$$
â Did
Sep 5 at 5:49
@Did: Looks like an answer to me?
â joriki
Sep 5 at 5:56
@joriki Free to use, anyway.
â Did
Sep 5 at 5:59
@Did if you may answer below, I would accept it. Sorry forsum
andSigma
. I used the same index because they are the same matrix. But I think I get your point.
â Jan
Sep 5 at 6:01
This "mess of indices" is already seen here. It is the source of problems.
â metamorphy
Sep 5 at 7:01
 |Â
show 1 more comment
3
Your notations are horrendous. First, what is $(Sigma_k W_ik H_kj)_ij$? Second, why do you use the same index in the outer sum and in the inner sum? Third, the symbol for sums issum
, notSigma
. What is right however is that $$sum_k fracW_ik H_kjsumlimits_ell W_iell H_ell j=frac1sumlimits_ell W_iell H_ell jsum_k W_ik H_kj=1$$
â Did
Sep 5 at 5:49
@Did: Looks like an answer to me?
â joriki
Sep 5 at 5:56
@joriki Free to use, anyway.
â Did
Sep 5 at 5:59
@Did if you may answer below, I would accept it. Sorry forsum
andSigma
. I used the same index because they are the same matrix. But I think I get your point.
â Jan
Sep 5 at 6:01
This "mess of indices" is already seen here. It is the source of problems.
â metamorphy
Sep 5 at 7:01
3
3
Your notations are horrendous. First, what is $(Sigma_k W_ik H_kj)_ij$? Second, why do you use the same index in the outer sum and in the inner sum? Third, the symbol for sums is
sum
, not Sigma
. What is right however is that $$sum_k fracW_ik H_kjsumlimits_ell W_iell H_ell j=frac1sumlimits_ell W_iell H_ell jsum_k W_ik H_kj=1$$â Did
Sep 5 at 5:49
Your notations are horrendous. First, what is $(Sigma_k W_ik H_kj)_ij$? Second, why do you use the same index in the outer sum and in the inner sum? Third, the symbol for sums is
sum
, not Sigma
. What is right however is that $$sum_k fracW_ik H_kjsumlimits_ell W_iell H_ell j=frac1sumlimits_ell W_iell H_ell jsum_k W_ik H_kj=1$$â Did
Sep 5 at 5:49
@Did: Looks like an answer to me?
â joriki
Sep 5 at 5:56
@Did: Looks like an answer to me?
â joriki
Sep 5 at 5:56
@joriki Free to use, anyway.
â Did
Sep 5 at 5:59
@joriki Free to use, anyway.
â Did
Sep 5 at 5:59
@Did if you may answer below, I would accept it. Sorry for
sum
and Sigma
. I used the same index because they are the same matrix. But I think I get your point.â Jan
Sep 5 at 6:01
@Did if you may answer below, I would accept it. Sorry for
sum
and Sigma
. I used the same index because they are the same matrix. But I think I get your point.â Jan
Sep 5 at 6:01
This "mess of indices" is already seen here. It is the source of problems.
â metamorphy
Sep 5 at 7:01
This "mess of indices" is already seen here. It is the source of problems.
â metamorphy
Sep 5 at 7:01
 |Â
show 1 more comment
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3
Your notations are horrendous. First, what is $(Sigma_k W_ik H_kj)_ij$? Second, why do you use the same index in the outer sum and in the inner sum? Third, the symbol for sums is
sum
, notSigma
. What is right however is that $$sum_k fracW_ik H_kjsumlimits_ell W_iell H_ell j=frac1sumlimits_ell W_iell H_ell jsum_k W_ik H_kj=1$$â Did
Sep 5 at 5:49
@Did: Looks like an answer to me?
â joriki
Sep 5 at 5:56
@joriki Free to use, anyway.
â Did
Sep 5 at 5:59
@Did if you may answer below, I would accept it. Sorry for
sum
andSigma
. I used the same index because they are the same matrix. But I think I get your point.â Jan
Sep 5 at 6:01
This "mess of indices" is already seen here. It is the source of problems.
â metamorphy
Sep 5 at 7:01