Matlab code that shows orthogonal functions

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Taylor Stafford
Taylor Stafford 2020-11-8
回答： Mathieu NOE 2020-11-10
Is there a way to write a code in matlab to show that given functions are orthogonal? For example, I have to write a matlab code that shows f1(x)=x^3 and f2(x)=x^2+1 to be orthogonal from the indicated intervals of [-1,1].

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Mathieu NOE
Mathieu NOE 2020-11-10
hi
functions are orthogonal if the integral of the product of the two function is zero on the x range (specified)
if you have to do it analytically, make the product (it's a polynomial) , write the integral of it (still a polynomial) and check the value of this integral over the x range.
this can be also checked numerically (with some rounding error) by :
x = [-1:1e-3:1];
y1 = x.^3;
y2 = x.^2+1;
prod = sum(y1.*y2); % zero (almost)

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