Question

The function 1,cos(x) , sin(x) , cos(2x), sin(2x),……. form the Fourier basis ( an infinite dimensional function space ). a)- write the 5x5 differentiation matrix for the first derivative of only those first five functions as a combination of the same five function b)- what is the kernel ( basis of null space) c)- what is image ( basis of the columns space).. If you can please help me with part (a) i can figure out part b and c

Answer 1

Combination part makes it difficult unless just take the derivative and put the multipliers in pivots

Answer 2

take the darivative and form a matrix but not like polynomial ,, be careful ..