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Reverse of Cauchy-Schuarz for two vectors [closed]
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If $|x|_2leq g|y|_2$, then according to Cauchy-Schuarz, the maximum of $ langle x,y rangle$ would be $ g|y|_2^2$
$$
langle x,y rangle leq g|y|_2^2
$$
Can we prove the reverse, i.e., if $langle x,y rangle leq g|y|_2^2$, then
$$
|x|_2leq g|y|_2
$$
linear-algebra inequality machine-learning
asked Jul 18 at 19:27
Saeed
887
closed as off-topic by Mostafa Ayaz, amWhy, Trần Thúc Minh TrÃ, Isaac Browne, user223391 Jul 19 at 14:06
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Mostafa Ayaz, amWhy, Trần Thúc Minh TrÃÂ, Isaac Browne, Community
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up vote
0
down vote
favorite
If $|x|_2leq g|y|_2$, then according to Cauchy-Schuarz, the maximum of $ langle x,y rangle$ would be $ g|y|_2^2$
$$
langle x,y rangle leq g|y|_2^2
$$
Can we prove the reverse, i.e., if $langle x,y rangle leq g|y|_2^2$, then
$$
|x|_2leq g|y|_2
$$
linear-algebra inequality machine-learning
asked Jul 18 at 19:27
Saeed
887
closed as off-topic by Mostafa Ayaz, amWhy, Trần Thúc Minh TrÃ, Isaac Browne, user223391 Jul 19 at 14:06
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Mostafa Ayaz, amWhy, Trần Thúc Minh TrÃÂ, Isaac Browne, Community
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If $|x|_2leq g|y|_2$, then according to Cauchy-Schuarz, the maximum of $ langle x,y rangle$ would be $ g|y|_2^2$
$$
langle x,y rangle leq g|y|_2^2
$$
Can we prove the reverse, i.e., if $langle x,y rangle leq g|y|_2^2$, then
$$
|x|_2leq g|y|_2
$$
linear-algebra inequality machine-learning
asked Jul 18 at 19:27
Saeed
887
If $|x|_2leq g|y|_2$, then according to Cauchy-Schuarz, the maximum of $ langle x,y rangle$ would be $ g|y|_2^2$
$$
langle x,y rangle leq g|y|_2^2
$$
Can we prove the reverse, i.e., if $langle x,y rangle leq g|y|_2^2$, then
$$
|x|_2leq g|y|_2
$$
linear-algebra inequality machine-learning
asked Jul 18 at 19:27
Saeed
887
asked Jul 18 at 19:27
Saeed
887
asked Jul 18 at 19:27
Saeed
887
asked Jul 18 at 19:27
Saeed
887
887
closed as off-topic by Mostafa Ayaz, amWhy, Trần Thúc Minh TrÃ, Isaac Browne, user223391 Jul 19 at 14:06
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Mostafa Ayaz, amWhy, Trần Thúc Minh TrÃÂ, Isaac Browne, Community
closed as off-topic by Mostafa Ayaz, amWhy, Trần Thúc Minh TrÃ, Isaac Browne, user223391 Jul 19 at 14:06
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Mostafa Ayaz, amWhy, Trần Thúc Minh TrÃÂ, Isaac Browne, Community
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1 Answer
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No -- if $x$ is orthogonal to $y$, we can make $x$ as big as we want but still have inner product $0$
answered Jul 18 at 19:29
Y. Forman
10.8k323
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
No -- if $x$ is orthogonal to $y$, we can make $x$ as big as we want but still have inner product $0$
answered Jul 18 at 19:29
Y. Forman
10.8k323
add a comment |Â
up vote
2
down vote
No -- if $x$ is orthogonal to $y$, we can make $x$ as big as we want but still have inner product $0$
answered Jul 18 at 19:29
Y. Forman
10.8k323
add a comment |Â
up vote
2
down vote
up vote
2
down vote
No -- if $x$ is orthogonal to $y$, we can make $x$ as big as we want but still have inner product $0$
answered Jul 18 at 19:29
Y. Forman
10.8k323
No -- if $x$ is orthogonal to $y$, we can make $x$ as big as we want but still have inner product $0$
answered Jul 18 at 19:29
Y. Forman
10.8k323
answered Jul 18 at 19:29
Y. Forman
10.8k323
answered Jul 18 at 19:29
Y. Forman
10.8k323
answered Jul 18 at 19:29
Y. Forman
10.8k323
10.8k323
add a comment |Â
add a comment |Â