Welcome to our site!

Electro Tech is an online community (with over 170,000 members) who enjoy talking about and building electronic circuits, projects and gadgets. To participate you need to register. Registration is free. Click here to register now.

  • Welcome to our site! Electro Tech is an online community (with over 170,000 members) who enjoy talking about and building electronic circuits, projects and gadgets. To participate you need to register. Registration is free. Click here to register now.

does it defines inner product..

Status
Not open for further replies.
does it defines inner product..(analisys)

C[0,2]\\
f:[0,2]->c\\
[latex]<f,g>=f(0)\overline{g(0)}+f(1)\overline{g(1)}+f(2)\overline{g(2)}[/latex]

i dont know how to solve the complement.
i tried to prove there easier version without the complement first.

<f,g>=f(0)g(0)+f(1)g(1)+f(2)g(2)\\
A.<g,f>=g(0)f(0)+g(1)f(1)+g(2)f(2)=f(0)g(0)+f(1)g(1)+f(2)g(2)=<f,g>
B.x<f,g>=x(f(0)g(0)+f(1)g(1)+f(2)g(2))=xf(0)g(0)+xf(1)g(1)+xf(2)g(2)=<xf,g>=<f,xg>

C.<x+y,g>=(x(0)+y(0))g(0)+(x(1)+y(1))g(1)+(x(2)+y(2))g(2)=<x,g>+<y,g>

step d:
<x,x>=x(0)x(0)+x(1)x(1)+x(2)x(2)

i dont know how to prove that
<x,x> greater or equal 0
i dont know the values of x
??
 
Last edited:

skyhawk

New Member
If x(0) is real, then x(0)x(0) > 0 because the square of any real number is positive, unless the number is zero.

Likewise x(1)y(1) > 0 and x(2)x(2) > 0 so <x,x> > 0 unless
x(0) = x(1) = x(2) = 0 in which case <x,x> = 0.
 
Last edited:

skyhawk

New Member
If x isn't real then you need the form of inner product that uses the complement (complex conjugate). Any number times its complex conjugate is greater than or equal to zero.
 
ok i tried to make the original question into easier one but i made it harder

actually the original question is:
[latex]<f,g>=f(0)\overline{g(0)}+f(1)\overline{g(1)}+f(2)\overline{g(2)}[/latex]

how to tackle the original one
?
 
Last edited:
Status
Not open for further replies.

EE World Online Articles

Loading
Top