Norm of V in ℂ^n Using Inner Product

P-Jay1
Messages
32
Reaction score
0
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
 
Physics news on Phys.org
Isn't that a row vector?

||V||=\sqrt{V*\cdot V}, where V* is the complex conjugate and the dot is the inner product.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
Back
Top