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"Show that the Triangle Inequality is an equality if and only if |a>=alpha|b> where alpha is a real positive scalar." It must be proved in both directions.

Any help on where to begin would be greatly appreciated.

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- Thread starter blanik
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- #1

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"Show that the Triangle Inequality is an equality if and only if |a>=alpha|b> where alpha is a real positive scalar." It must be proved in both directions.

Any help on where to begin would be greatly appreciated.

- #2

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blanik said:

"Show that the Triangle Inequality is an equality if and only if |a>=alpha|b> where alpha is a real positive scalar." It must be proved in both directions.

Any help on where to begin would be greatly appreciated.

begin by proving one direction. complete the proof by proving the other direction. i'm not sure what |a>=alpha|b> means, is there another way to explain what that says?

- #3

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I understand that I am "supposed" to start with one way and go the other, but what does that mean? Do I substitute a=alpha b for a and solve for ||alpha b + b|| = ||alpha b|| + ||b||? I have been playing around with the definition of ||a|| = SQRT (a a*), etc...

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