Questions from Abbas Edalat's notes(adsbygoogle = window.adsbygoogle || []).push({});

http://www.doc.ic.ac.uk/~ae/teaching.html#quantum"

It's about vector space, linear independence and linear dependence of vectors or something else.

Thanks!

Generalize the following notions and properties given for the vector space C^2 in the notes to C^d.

1) Define the norm \omega of a vector and the inner product of two vectors \omega(1) and \omega(2) in C^d. What is the dual of a vector \omega in C^d and what can it be identified with?

2) Define linear independence and linear dependence of vectors in C^d.

3) What is the least integer n such that any set of n vectors in C^d will be linearly dependent?

4) What is a basis of C^d? How many linearly independent vectors it takes to get a basis for C^d?

5) Define the notion of an orthonormal basis for C^d. What would be the standard basis of C^d?

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