Mixing
Expressing a function in terms of another
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I know this is a very nonsense question. But, it has become challenging for me to visualize. I have two functions as seen following:
$$rho=sum_jin Jfraclambda_jmu_j$$
and
$$theta=sum_jin Jfraclambda_jmu_j^2$$
Is there any way to express $theta$ in terms of $rho$ or vice versa?
functional-analysis
asked Jul 25 at 16:14
user8028576
277
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up vote
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I know this is a very nonsense question. But, it has become challenging for me to visualize. I have two functions as seen following:
$$rho=sum_jin Jfraclambda_jmu_j$$
and
$$theta=sum_jin Jfraclambda_jmu_j^2$$
Is there any way to express $theta$ in terms of $rho$ or vice versa?
functional-analysis
asked Jul 25 at 16:14
user8028576
277
1
I would say, "No." How would you express $frac1a+frac1b$ in terms of $frac1a^2+frac1b^2?$
– saulspatz
Jul 25 at 16:18
I also said, "No" and that's why I wanted to get more opinions. On the other hand, it seems, I can write $theta = sum_jin Jfraclambda_jmu_jfrac1mu_j stackrel?= frac1mu_jsum_jin Jfraclambda_jmu_j$. Then, what is gonna happen with $frac1mu_j$?
– user8028576
Jul 25 at 16:24
You can't pull $1/u_j$ out of the summation sign. Its value is different in every term of the sum.
– saulspatz
Jul 25 at 16:28
@saulspatz, I am well aware of that. Just trying to put here something to get help if there is any possible way of doing that.
– user8028576
Jul 25 at 16:30
My best attempt: $$theta= - sum_j in J fracpartialpartial mu_j rho$$ but it's really not easier than just writing $$theta = sum_j in J fraclambda_jmu_j^2.$$
– md2perpe
Jul 25 at 18:29
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I know this is a very nonsense question. But, it has become challenging for me to visualize. I have two functions as seen following:
$$rho=sum_jin Jfraclambda_jmu_j$$
and
$$theta=sum_jin Jfraclambda_jmu_j^2$$
Is there any way to express $theta$ in terms of $rho$ or vice versa?
functional-analysis
asked Jul 25 at 16:14
user8028576
277
I know this is a very nonsense question. But, it has become challenging for me to visualize. I have two functions as seen following:
$$rho=sum_jin Jfraclambda_jmu_j$$
and
$$theta=sum_jin Jfraclambda_jmu_j^2$$
Is there any way to express $theta$ in terms of $rho$ or vice versa?
functional-analysis
asked Jul 25 at 16:14
user8028576
277
edited Jul 25 at 16:38
asked Jul 25 at 16:14
user8028576
277
asked Jul 25 at 16:14
user8028576
277
asked Jul 25 at 16:14
user8028576
277
277
1
I would say, "No." How would you express $frac1a+frac1b$ in terms of $frac1a^2+frac1b^2?$
– saulspatz
Jul 25 at 16:18
I also said, "No" and that's why I wanted to get more opinions. On the other hand, it seems, I can write $theta = sum_jin Jfraclambda_jmu_jfrac1mu_j stackrel?= frac1mu_jsum_jin Jfraclambda_jmu_j$. Then, what is gonna happen with $frac1mu_j$?
– user8028576
Jul 25 at 16:24
You can't pull $1/u_j$ out of the summation sign. Its value is different in every term of the sum.
– saulspatz
Jul 25 at 16:28
@saulspatz, I am well aware of that. Just trying to put here something to get help if there is any possible way of doing that.
– user8028576
Jul 25 at 16:30
My best attempt: $$theta= - sum_j in J fracpartialpartial mu_j rho$$ but it's really not easier than just writing $$theta = sum_j in J fraclambda_jmu_j^2.$$
– md2perpe
Jul 25 at 18:29
add a comment |Â
1
I would say, "No." How would you express $frac1a+frac1b$ in terms of $frac1a^2+frac1b^2?$
– saulspatz
Jul 25 at 16:18
I also said, "No" and that's why I wanted to get more opinions. On the other hand, it seems, I can write $theta = sum_jin Jfraclambda_jmu_jfrac1mu_j stackrel?= frac1mu_jsum_jin Jfraclambda_jmu_j$. Then, what is gonna happen with $frac1mu_j$?
– user8028576
Jul 25 at 16:24
You can't pull $1/u_j$ out of the summation sign. Its value is different in every term of the sum.
– saulspatz
Jul 25 at 16:28
@saulspatz, I am well aware of that. Just trying to put here something to get help if there is any possible way of doing that.
– user8028576
Jul 25 at 16:30
My best attempt: $$theta= - sum_j in J fracpartialpartial mu_j rho$$ but it's really not easier than just writing $$theta = sum_j in J fraclambda_jmu_j^2.$$
– md2perpe
Jul 25 at 18:29
1
1
I would say, "No." How would you express $frac1a+frac1b$ in terms of $frac1a^2+frac1b^2?$
– saulspatz
Jul 25 at 16:18
I would say, "No." How would you express $frac1a+frac1b$ in terms of $frac1a^2+frac1b^2?$
– saulspatz
Jul 25 at 16:18
I also said, "No" and that's why I wanted to get more opinions. On the other hand, it seems, I can write $theta = sum_jin Jfraclambda_jmu_jfrac1mu_j stackrel?= frac1mu_jsum_jin Jfraclambda_jmu_j$. Then, what is gonna happen with $frac1mu_j$?
– user8028576
Jul 25 at 16:24
I also said, "No" and that's why I wanted to get more opinions. On the other hand, it seems, I can write $theta = sum_jin Jfraclambda_jmu_jfrac1mu_j stackrel?= frac1mu_jsum_jin Jfraclambda_jmu_j$. Then, what is gonna happen with $frac1mu_j$?
– user8028576
Jul 25 at 16:24
You can't pull $1/u_j$ out of the summation sign. Its value is different in every term of the sum.
– saulspatz
Jul 25 at 16:28
You can't pull $1/u_j$ out of the summation sign. Its value is different in every term of the sum.
– saulspatz
Jul 25 at 16:28
@saulspatz, I am well aware of that. Just trying to put here something to get help if there is any possible way of doing that.
– user8028576
Jul 25 at 16:30
@saulspatz, I am well aware of that. Just trying to put here something to get help if there is any possible way of doing that.
– user8028576
Jul 25 at 16:30
My best attempt: $$theta= - sum_j in J fracpartialpartial mu_j rho$$ but it's really not easier than just writing $$theta = sum_j in J fraclambda_jmu_j^2.$$
– md2perpe
Jul 25 at 18:29
My best attempt: $$theta= - sum_j in J fracpartialpartial mu_j rho$$ but it's really not easier than just writing $$theta = sum_j in J fraclambda_jmu_j^2.$$
– md2perpe
Jul 25 at 18:29
add a comment |Â
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1
I would say, "No." How would you express $frac1a+frac1b$ in terms of $frac1a^2+frac1b^2?$
– saulspatz
Jul 25 at 16:18
I also said, "No" and that's why I wanted to get more opinions. On the other hand, it seems, I can write $theta = sum_jin Jfraclambda_jmu_jfrac1mu_j stackrel?= frac1mu_jsum_jin Jfraclambda_jmu_j$. Then, what is gonna happen with $frac1mu_j$?
– user8028576
Jul 25 at 16:24
You can't pull $1/u_j$ out of the summation sign. Its value is different in every term of the sum.
– saulspatz
Jul 25 at 16:28
@saulspatz, I am well aware of that. Just trying to put here something to get help if there is any possible way of doing that.
– user8028576
Jul 25 at 16:30
My best attempt: $$theta= - sum_j in J fracpartialpartial mu_j rho$$ but it's really not easier than just writing $$theta = sum_j in J fraclambda_jmu_j^2.$$
– md2perpe
Jul 25 at 18:29