Mixing
Positive Definiteness of Arcsin of a Positve Definite Matrix [closed]
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Suppose that $M$ is a positive definite matrix with entries within $[-1,1]$, and let $N$ be a matrix where $N_{ij} = sin^{-1}M_{ij}$. How do I show that $N$ is also positive definite?
linear-algebra normal-distribution positive-definite
asked Jan 27 at 21:51
Sudeshna GargSudeshna Garg
61
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closed as off-topic by max_zorn, Cesareo, Gibbs, Lee David Chung Lin, onurcanbektas Jan 28 at 8:13
This question appears to be off-topic. The users who voted to close gave this specific reason:
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$begingroup$
Suppose that $M$ is a positive definite matrix with entries within $[-1,1]$, and let $N$ be a matrix where $N_{ij} = sin^{-1}M_{ij}$. How do I show that $N$ is also positive definite?
linear-algebra normal-distribution positive-definite
asked Jan 27 at 21:51
Sudeshna GargSudeshna Garg
61
$endgroup$
closed as off-topic by max_zorn, Cesareo, Gibbs, Lee David Chung Lin, onurcanbektas Jan 28 at 8:13
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – max_zorn, Cesareo, Gibbs, Lee David Chung Lin, onurcanbektas
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Suppose that $M$ is a positive definite matrix with entries within $[-1,1]$, and let $N$ be a matrix where $N_{ij} = sin^{-1}M_{ij}$. How do I show that $N$ is also positive definite?
linear-algebra normal-distribution positive-definite
asked Jan 27 at 21:51
Sudeshna GargSudeshna Garg
61
$endgroup$
Suppose that $M$ is a positive definite matrix with entries within $[-1,1]$, and let $N$ be a matrix where $N_{ij} = sin^{-1}M_{ij}$. How do I show that $N$ is also positive definite?
linear-algebra normal-distribution positive-definite
linear-algebra normal-distribution positive-definite
asked Jan 27 at 21:51
Sudeshna GargSudeshna Garg
61
asked Jan 27 at 21:51
Sudeshna GargSudeshna Garg
61
asked Jan 27 at 21:51
Sudeshna GargSudeshna Garg
61
asked Jan 27 at 21:51
Sudeshna GargSudeshna Garg
61
asked Jan 27 at 21:51
Sudeshna GargSudeshna Garg
61
61
closed as off-topic by max_zorn, Cesareo, Gibbs, Lee David Chung Lin, onurcanbektas Jan 28 at 8:13
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – max_zorn, Cesareo, Gibbs, Lee David Chung Lin, onurcanbektas
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by max_zorn, Cesareo, Gibbs, Lee David Chung Lin, onurcanbektas Jan 28 at 8:13
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – max_zorn, Cesareo, Gibbs, Lee David Chung Lin, onurcanbektas
If this question can be reworded to fit the rules in the help center, please edit the question.
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1 Answer
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This follows from the facts that the element-wise product of p.s.d. matrices is p.s.d, that the sum of p.s.d. matrices is p.s.d., and that the Taylor series for $arcsin$ has non-negative terms.
answered Jan 27 at 22:03
kimchi loverkimchi lover
11.5k31229
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
This follows from the facts that the element-wise product of p.s.d. matrices is p.s.d, that the sum of p.s.d. matrices is p.s.d., and that the Taylor series for $arcsin$ has non-negative terms.
answered Jan 27 at 22:03
kimchi loverkimchi lover
11.5k31229
$endgroup$
add a comment |
$begingroup$
This follows from the facts that the element-wise product of p.s.d. matrices is p.s.d, that the sum of p.s.d. matrices is p.s.d., and that the Taylor series for $arcsin$ has non-negative terms.
answered Jan 27 at 22:03
kimchi loverkimchi lover
11.5k31229
$endgroup$
add a comment |
$begingroup$
This follows from the facts that the element-wise product of p.s.d. matrices is p.s.d, that the sum of p.s.d. matrices is p.s.d., and that the Taylor series for $arcsin$ has non-negative terms.
answered Jan 27 at 22:03
kimchi loverkimchi lover
11.5k31229
$endgroup$
This follows from the facts that the element-wise product of p.s.d. matrices is p.s.d, that the sum of p.s.d. matrices is p.s.d., and that the Taylor series for $arcsin$ has non-negative terms.
answered Jan 27 at 22:03
kimchi loverkimchi lover
11.5k31229
edited Jan 27 at 22:12
answered Jan 27 at 22:03
kimchi loverkimchi lover
11.5k31229
answered Jan 27 at 22:03
kimchi loverkimchi lover
11.5k31229
answered Jan 27 at 22:03
kimchi loverkimchi lover
11.5k31229
11.5k31229
add a comment |
add a comment |
