Please check my work on inner product operation

[iScience]

i realize this is a linear algebra question, but the bra-ket notation is still a little confusing to me so i posted it in this section.


|e>=(1+i,1,i) (n-tuple representation, where i's are the imaginaries)

so the norm of this would then be the following?

||e||=$$\sqrt{<e|e>}$$=$$\sqrt{(1+i,1,i)\cdot(1+i,1,i)}$$=$$\sqrt{(1+2i+i^2)+1+i^2}$$=$$\sqrt{2i}$$

 

[jedishrfu]

looks good.

It seems that you can extract the sqrt(i) from the sqrt though:

http://www.math.toronto.edu/mathnet/questionCorner/rootofi.html

 

[Dick]

i realize this is a linear algebra question, but the bra-ket notation is still a little confusing to me so i posted it in this section.


|e>=(1+i,1,i) (n-tuple representation, where i's are the imaginaries)

so the norm of this would then be the following?

||e||=$$\sqrt{<e|e>}$$=$$\sqrt{(1+i,1,i)\cdot(1+i,1,i)}$$=$$\sqrt{(1+2i+i^2)+1+i^2}$$=$$\sqrt{2i}$$

No, it's not right. If |e>=(1+i,1,i) then <e| is the hermitian conjugate vector. You forgot the complex conjugation. <e|e> should be a real number.