Hi,

how can one shows that an orthonomal set in an inner product space is automatically an independent set?

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- May 4th 2010, 12:50 PMmtmathorthonomal set
Hi,

how can one shows that an orthonomal set in an inner product space is automatically an independent set? - May 4th 2010, 01:58 PMtonio
- May 5th 2010, 03:13 AMmtmath
- May 5th 2010, 03:29 AMHallsofIvy
Yes, and since it is "not linearly dependent", it is linearly independent.

- May 5th 2010, 04:25 AMtonio

Well,such summation is zero when all the coefficients are zero...(Worried)...what you wanted to prove, and we achieved, is that__any__then the sum is zero, or in other words: if the sum is zero then all the coefficients equal zero. This, according to definition, means the vectors are lin.__only__.__independient__

Tonio