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Exercise 4.4.2

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Suppose matrix $D$ has eigenvalues of $λ$ and eigenvectors of $u$ ,

For $K = I \otimes D + D \otimes I = I \oplus D$ , from Kronecker section IV.3, the eigenvalues of $K$ are $ $λ_{i j} = λ_i + λ_j = 2 (\cos \frac{(i + j) π h}{N + 1} - 2) $ a n d e i g e n v e c t o r s a r e : u ij = u i ⊗ u j$

niuers

2020-03-20 00:00

Exercise 4.4.2

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