Question: Linear Algebra Let n be a natural number. Let V = span { sin x, cosa, sin(2x), cos(2x), ..., sin(no), cos(no) }, where complex numbers

Linear Algebra

Let n be a natural number. Let V = span { sin x, cosa, sin(2x), cos(2x), ..., sin(no), cos(no) }, where complex numbers are used for coefficients of linear combinations. Let Te C(V) de- note the operator , which is the first order derivative. Prove that ?' is diagonalizable. Hint: Find the eigenvalues and eigenvectors of T

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