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12 Nov 2019
It is also possible to define functions as being orthogonal if we can find the correct definition to replace the dot product. If we take two functions f and g, defined over the interval [0, 2 pi], then we can define a fancy inner product = integral^2 pi_0 f(x) g(x) dx. This will play the same role as the dot product, taking two vectors as input and spitting out a number. Using this, we define two functions to be orthogonal if = 0, The same way we do for geometric vectors. Let's consider the functions f(x) = sin(3x), g(x) = sin(2x). Using the inner product definition above we can determine = integral^2 pi_0 sin(3x)sin(2x) dx = 0 = integral^2 pi_0 (sin(3x))^2 dx = = integral^2 pi_0 (sin(2x))^2 dx = Showing that f(x) = sin(3x) and g(x) = sin(2x) are orthogonal with respect to this cool new product
It is also possible to define functions as being orthogonal if we can find the correct definition to replace the dot product. If we take two functions f and g, defined over the interval [0, 2 pi], then we can define a fancy inner product = integral^2 pi_0 f(x) g(x) dx. This will play the same role as the dot product, taking two vectors as input and spitting out a number. Using this, we define two functions to be orthogonal if = 0, The same way we do for geometric vectors. Let's consider the functions f(x) = sin(3x), g(x) = sin(2x). Using the inner product definition above we can determine = integral^2 pi_0 sin(3x)sin(2x) dx = 0 = integral^2 pi_0 (sin(3x))^2 dx = = integral^2 pi_0 (sin(2x))^2 dx = Showing that f(x) = sin(3x) and g(x) = sin(2x) are orthogonal with respect to this cool new product
Casey DurganLv2
31 Oct 2019