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If P is a n x 1 matrix such that P( ^T)*P = 1 and H = I - 2PP(^T), then H(^T)*H is ?

Note :

A(^T) means the transpose of matrix A.

Confusion:

What I don't get is are we supposed to do I (identity matrix-I'm assuming of order 1 x 1) - 2 ? If that is the way we're supposed to do the question then are we supposed to treat 2 as a 1 x 1 matrix. If that's the case then is the following correct:

Since P( ^t)*P = PP(^T) = 1 = [1]

So,

H = I - 2PP(^T) = I - 2PP(^T) = I - 2[1] = [1] - [2] =[-1]

thus,

H(^T)*H = [-1] * [-1](^T) = [-1] * [-1] = [1]

Help?

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# What will H(^T)*H be?

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