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Eigenvalues & Eigenvectorsmedium
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Let V=span{sin⁡x,cos⁡x}V = \text{span}\{\sin x, \cos x\}V=span{sinx,cosx} be a vector space over R\mathbb{R}R. Let D:V→VD: V \to VD:V→V be the linear transformation defined by the derivative operator, D(f)=f′D(f) = f'D(f)=f′. What are the eigenvalues of the matrix representation of DDD over the complex numbers C\mathbb{C}C?