Norm of V in ℂ^n Using Inner Product

Thread starter P-Jay1
Start date Oct 12, 2011
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SUMMARY

The norm of the vector V = (1, i) in ℂ^n is calculated using the standard inner product, defined as ||V|| = √(V* · V), where V* represents the complex conjugate of V. In this case, V* = (1, -i), leading to the calculation ||V|| = √((1)(1) + (i)(-i)) = √(1 + 1) = √2. This confirms that V is indeed a row vector, and the inner product method accurately computes its norm.

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Understanding of complex numbers and their conjugates
Familiarity with inner product spaces
Knowledge of matrix representation of vectors
Basic principles of vector norms

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Oct 12, 2011

P-Jay1

Using the standard inner product in ℂ^n how would I calculate the norm of:

V= ( 1 , i ) , where this is a 1 x 2 matrix

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Oct 12, 2011

DiracRules

Isn't that a row vector?

||V||=\sqrt{V*\cdot V}, where V* is the complex conjugate and the dot is the inner product.

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