- #1
Asuralm
- 35
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Dear all:
I have a problem about the inner product of a function. Give a function
[tex]
\begin{displaymath}
f(x) = \left\{ \begin{array}{ll}
x & \textrm{if $x \in [0,1]$}\\
-x+2 & \textrm{if $x \in (1, 2]$}
\end{array}
\end{displaymath}
\{[/tex]
What's the value of the inner product of the function itself over [0,2]?
[tex]
\begin{displaymath}
<f(x), f(x)> = \int_{x=0}^{x=2} f(x)f(x) d_x
\end{displaymath}
[/tex]]
If given another function
[tex]
g(x) = \left\{ \begin{array}{ll}
x-1 & \textrm{if $x \in [1,2]$}\\
-x+3 & \textrm{if $x \in (2, 3]$}
\end{array}
\{[/tex]
What's the inner product of f(x) and g(x) please?
Thanks for answering.
I have a problem about the inner product of a function. Give a function
[tex]
\begin{displaymath}
f(x) = \left\{ \begin{array}{ll}
x & \textrm{if $x \in [0,1]$}\\
-x+2 & \textrm{if $x \in (1, 2]$}
\end{array}
\end{displaymath}
\{[/tex]
What's the value of the inner product of the function itself over [0,2]?
[tex]
\begin{displaymath}
<f(x), f(x)> = \int_{x=0}^{x=2} f(x)f(x) d_x
\end{displaymath}
[/tex]]
If given another function
[tex]
g(x) = \left\{ \begin{array}{ll}
x-1 & \textrm{if $x \in [1,2]$}\\
-x+3 & \textrm{if $x \in (2, 3]$}
\end{array}
\{[/tex]
What's the inner product of f(x) and g(x) please?
Thanks for answering.
Last edited: