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
edited Sep 10 at 20:19
Did
243k23209445
asked Sep 5 at 5:40
Jan
1747
 |Â
show 1 more comment
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
edited Sep 10 at 20:19
Did
243k23209445
asked Sep 5 at 5:40
Jan
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 $$sum_k fracW_ik H_kjsumlimits_ell W_iell H_ell j=frac1sumlimits_ell W_iell H_ell jsum_k W_ik H_kj=1$$
– Did
Sep 5 at 5:49
@Did: Looks like an answer to me?
– joriki
Sep 5 at 5:56
@joriki Free to use, anyway.
– Did
Sep 5 at 5:59
@Did if you may answer below, I would accept it. Sorry forsumandSigma. I used the same index because they are the same matrix. But I think I get your point.
– Jan
Sep 5 at 6:01
This "mess of indices" is already seen here. It is the source of problems.
– 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
edited Sep 10 at 20:19
Did
243k23209445
asked Sep 5 at 5:40
Jan
1747
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
asked Sep 5 at 5:40
Jan
1747
edited Sep 10 at 20:19
Did
243k23209445
asked Sep 5 at 5:40
Jan
1747
edited Sep 10 at 20:19
Did
243k23209445
edited Sep 10 at 20:19
Did
243k23209445
edited Sep 10 at 20:19
Did
243k23209445
243k23209445
asked Sep 5 at 5:40
Jan
1747
asked Sep 5 at 5:40
Jan
1747
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 $$sum_k fracW_ik H_kjsumlimits_ell W_iell H_ell j=frac1sumlimits_ell W_iell H_ell jsum_k W_ik H_kj=1$$
– Did
Sep 5 at 5:49
@Did: Looks like an answer to me?
– joriki
Sep 5 at 5:56
@joriki Free to use, anyway.
– Did
Sep 5 at 5:59
@Did if you may answer below, I would accept it. Sorry forsumandSigma. I used the same index because they are the same matrix. But I think I get your point.
– Jan
Sep 5 at 6:01
This "mess of indices" is already seen here. It is the source of problems.
– 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 $$sum_k fracW_ik H_kjsumlimits_ell W_iell H_ell j=frac1sumlimits_ell W_iell H_ell jsum_k W_ik H_kj=1$$
– Did
Sep 5 at 5:49
@Did: Looks like an answer to me?
– joriki
Sep 5 at 5:56
@joriki Free to use, anyway.
– Did
Sep 5 at 5:59
@Did if you may answer below, I would accept it. Sorry forsumandSigma. I used the same index because they are the same matrix. But I think I get your point.
– Jan
Sep 5 at 6:01
This "mess of indices" is already seen here. It is the source of problems.
– 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 $$sum_k fracW_ik H_kjsumlimits_ell W_iell H_ell j=frac1sumlimits_ell W_iell H_ell jsum_k W_ik H_kj=1$$– 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 $$sum_k fracW_ik H_kjsumlimits_ell W_iell H_ell j=frac1sumlimits_ell W_iell H_ell jsum_k W_ik H_kj=1$$– Did
Sep 5 at 5:49
@Did: Looks like an answer to me?
– joriki
Sep 5 at 5:56
@Did: Looks like an answer to me?
– joriki
Sep 5 at 5:56
@joriki Free to use, anyway.
– Did
Sep 5 at 5:59
@joriki Free to use, anyway.
– 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.– 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.– Jan
Sep 5 at 6:01
This "mess of indices" is already seen here. It is the source of problems.
– metamorphy
Sep 5 at 7:01
This "mess of indices" is already seen here. It is the source of problems.
– 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 $$sum_k fracW_ik H_kjsumlimits_ell W_iell H_ell j=frac1sumlimits_ell W_iell H_ell jsum_k W_ik H_kj=1$$– Did
Sep 5 at 5:49
@Did: Looks like an answer to me?
– joriki
Sep 5 at 5:56
@joriki Free to use, anyway.
– Did
Sep 5 at 5:59
@Did if you may answer below, I would accept it. Sorry for
sumandSigma. I used the same index because they are the same matrix. But I think I get your point.– Jan
Sep 5 at 6:01
This "mess of indices" is already seen here. It is the source of problems.
– metamorphy
Sep 5 at 7:01