The Rook on the Half - Chessboard , or
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چکیده
منابع مشابه
The Rook on the Half-Chessboard, or How Not to Diagonalize a Matrix
1/i if i + j ≥ n + 1 0 otherwise, has eigenvalues 1,−1/2, 1/3, . . . , (−1)/n. In Section 2, we establish this result in two ways: (1) by explicitly exhibiting eigenvectors via an odd-looking combinatorial identity, and (2) by giving a matrix that conjugates Tn into an upper triangular matrix. In Section 3, we use the knowledge of the eigenvalues of Tn to study two related random walks, most co...
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