be an orthonormal set in Rn. Verify the following

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QUESTION:

Problem 3E

be an orthonormal set in Rn. Verify the following inequality, called Bessel’s inequality, which is true for each x in Rn:

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QUESTION:

Problem 3E

be an orthonormal set in Rn. Verify the following inequality, called Bessel’s inequality, which is true for each x in Rn:

ANSWER:

Solution 3E

Step 1 of 2

It is stated that the set of vectors  is orthonormal set in.

The magnitude of each vector is equals to 1 and dot product of each pair of vectors is equals to 0.

It can be expressed as,

Let  be the orthogonal projection of  onto the subspace spanned by.

Then  

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