Questions, Week 8 Notes

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Posted by Michael on November 29, 2002 at 23:31:55:

On page 23, should the result be ||cv|| = |c| ||v|| instead of |c| |v|? If v is a vector, does |v| have any meaning, or just ||v||?

On page 24, can we say -c ||v||^2 = -||v|| ||-cv|| only because we know ||-cv|| = ||cv||, and thus -||v|| ||-cv|| = -||v|| ||cv|| = -||v|| c ||v|| = -c ||v||^2?

On page 25, you say |a|^2 ||v||^2 + ab' + ba' ' + |b|^2 ||w||^2 is positive for any choice of scalars a, b. I understand how the first and last terms, because they are squared, are non-negative, and since the sum is greater than 0 then we must have |a|^2 ||v||^2 + |b|^2 ||w||^2 > ab' + ba' '. But i don't understand why this is true.

Thanks,

Michael

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Re: Questions, Week 8 Notes Terence Tao 20:03:43 12/01/2002 (0)

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>On page 23, should the result be ||cv|| = |c| ||v|| instead of |c| |v|? If v is a vector, does |v| have any meaning, or just ||v||? >On page 24, can we say -c ||v||^2 = -||v|| ||-cv|| only because we know ||-cv|| = ||cv||, and thus -||v|| ||-cv|| = -||v|| ||cv|| = -||v|| c ||v|| = -c ||v||^2? >On page 25, you say |a|^2 ||v||^2 + ab' <v,w> + ba' <v,w>' + |b|^2 ||w||^2 is positive for any choice of scalars a, b. I understand how the first and last terms, because they are squared, are non-negative, and since the sum is greater than 0 then we must have |a|^2 ||v||^2 + |b|^2 ||w||^2 > ab' <v,w> + ba' <v,w>'. But i don't understand why this is true. >Thanks, >Michael

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