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A tridiagonal matrix is a band matrix that has nonzero elements only on the main diagonal, the first diagonal below this, and the first diagonal above the main diagonal.

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Eigenvalues of symmetric tridiagonal matrices

According to doi:10.1016/S0024-3795(99)00114-7, the closed form for the eigenvalues of a tridiagonal Toepliz matrix of the form $$ \begin{bmatrix}a & b\\ c & a & b\\ & \ddots & a & \ddots \\ & & …
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