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{c}

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.


Toeplitz antisymmetric tridiagonal matrix

Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 3 / 40E / b / Solution

Toeplitz antisymmetric tridiagonal matrix

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Toeplitz antisymmetric tridiagonal matrix

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