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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.

- 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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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?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.

- #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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Galileo

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