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?










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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, 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










  • @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










  • This "mess of indices" is already seen here. It is the source of problems.
    – metamorphy
    Sep 5 at 7:01














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?










share|cite|improve this question



















  • 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











  • @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 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












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?










share|cite|improve this question















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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








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 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










  • @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










  • This "mess of indices" is already seen here. It is the source of problems.
    – metamorphy
    Sep 5 at 7:01












  • 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











  • @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 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







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















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