Let (V ; <,>) be a Euclidean space and let x, y and z be nonzero vectors of V . Prove that:

[vicsan21]

Let (V ; <,>) be a Euclidean space and let x, y and z be nonzero vectors of V . Prove that:
They tell us that we must use the Schwarz inequality in the particular case of the usual Euclidean space R^3:
Therefore, it is a question of conveniently choosing ?1, ?2, ?3 and ?1, ?2, ?3 so that, Using the previous inequality, we arrive at, or at least get very close to, the inequality proposed in the statement. The cyclical nature of the sums must be taken into account.

 

[stapel]

Let (V ; <,>) be a Euclidean space and let x, y and z be nonzero vectors of V . Prove that:View attachment 35968
They tell us that we must use the Schwarz inequality in the particular case of the usual Euclidean space R^3:View attachment 35969
Therefore, it is a question of conveniently choosing ?1, ?2, ?3 and ?1, ?2, ?3 so that, Using the previous inequality, we arrive at, or at least get very close to, the inequality proposed in the statement. The cyclical nature of the sums must be taken into account.

What are your thoughts? What have you tried? How far have you gotten?

Please be complete, even if you think your work is wrong. Thank you!

 

[vicsan21]

What are your thoughts? What have you tried? How far have you gotten?

Please be complete, even if you think your work is wrong. Thank you!

I don't have any idea of how to start the problem.

 

[blamocur]

Let (V ; <,>) be a Euclidean space and let x, y and z be nonzero vectors of V . Prove that:View attachment 35968
They tell us that we must use the Schwarz inequality in the particular case of the usual Euclidean space R^3:View attachment 35969
Therefore, it is a question of conveniently choosing ?1, ?2, ?3 and ?1, ?2, ?3 so that, Using the previous inequality, we arrive at, or at least get very close to, the inequality proposed in the statement. The cyclical nature of the sums must be taken into account.

What does "cíclica" mean?
Also, am I correct to assume that "<x,y>" means dot product of x and y ?
Thanks.

 

[khansaheb]

I don't have any idea of how to start the problem.

What about the example problems of the chapter in your textbook?

Which text book is being used in the classroom?

 

[khansaheb]

I don't have any idea of how to start the problem.

What does "cíclica" mean?

In addition, according to your textbook, please provide the definition of

the Schwarz inequality in the particular case of the usual Euclidean space R^3

Then we would have some idea of what we can assume "should be your starting point".

 

[blamocur]

In addition, according to your textbook, please provide the definition of

Then we would have some idea of what we can assume "should be your starting point".

Is not the formula for Schwarz inequality in the original post? I.e, that the absolute value of the dot product never exceeds the product of the norms.

 

[khansaheb]

Is not the formula for Schwarz inequality in the original post? I.e, that the absolute value of the dot product never exceeds the product of the norms.

Correct - But I was hoping after ~15 days of silence since posting, the OP will confirm that (and we will know s/he at least knows THAT)

 

[blamocur]

Correct - But I was hoping after ~15 days of silence since posting, the OP will confirm that (and we will know s/he at least knows THAT)

I was hoping too Unfortunately there are quite a few threads in this forum where the OP dumps a problem, most likely from homework, hoping to get a ready-to-copy solution. I keep reminding myself to ignore such threads.