Quick question (hopefully) on Matlab transfer functions

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In MATLAB, the transfer function is defined using the syntax s = tf('s') to create the variable 's', which is essential for constructing transfer functions. The expression H = s/(s^2 + 2*s + 10) assigns the transfer function to the variable H, which is arbitrary and can be named differently without affecting the function itself. The significance of 'H' lies in its common use in control theory to represent the transfer function. The relationship is clarified by the output equation Y(s) = H(s) x U(s), illustrating that H represents the system's response to an input U(s). Understanding this connection helps in utilizing transfer functions effectively in MATLAB.
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Homework Statement



I'm reading through the help files and came across this example:

s = tf('s');
H = s/(s^2 + 2*s +10);

I understand that when using a rational expression it must be specified, s= tf('s');

I also understand that the rational expression is entered through H=s/(s^2 + 2*s +10);

I'm just struggling a bit with how these two expressions connect to each other. To me it looks like s/(s^2 + 2*s +10) is being saved as H, but there is no H in the first expression. Is H arbitrary? Could s/(s^2 + 2*s +10) be saved under any name or is there significance in the letter H?
 
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OK, think I have it...

output, Y(s) = transfer function, H(s) x Input, U(s) so H is naming the transfer function within Matlab and this is the connection.
 
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