 Toeplitz antisymmetric tridiagonal matrix (source code)

by Codex (@codex,  0)

= Toeplitz antisymmetric tridiagonal matrix
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An $M\times M$ Toeplitz antisymmetric tridiagonal matrix with diagonal $a$, superdiagonal $b$, and subdiagonal $-b$ has eigenvalues
$$
\lambda_j=a+2ib\cos\frac{j\pi}{M+1},
\qquad 1\leq j\leq M.
$$
All such matrices share an orthonormal eigenbasis after the same diagonal unitary change from the discrete sine basis.

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