# tridiagonal matrix

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## tridiagonal matrix

[¦trī·dī′ag·ən·əl ′mā·triks]
(mathematics)
A square matrix in which all entries other than those on the principal diagonal and the two adjacent diagonals are zero.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
This also means that for any irreducible tridiagonal matrix [T.sub.n], there exists a linear functional C quasi-definite on [P.sub.n-1] such that [T.sub.n] is determined by the first 2n moments of C.
Table 1: Condition numbers for Example 1 evaluated using different tridiagonal matrices with size n.
Znojil, "Tridiagonal PT-symmetric N-by-N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime," Journal of PhysicsA: Mathematical and Theoretical, vol.
Similarly, the vectors [[psi].sup.(od).sub.m] (j), j = 1, ..., M, are the eigenstates of the tridiagonal M x M matrix [H.sup.(od)]:
Zhang, "Stability of nonlinear systems with tridiagonal structure and its applications," Acta Automatica Sinica, vol.
The solution in the (n + 1)th time step is obtained by solving the below block tridiagonal system:
(34) using centered differences for the differential operator and a quadrature formula for the integral operator produces a dense matrix rather than a tridiagonal matrix, but this problem is still amenable to solution with a conventional eigensolver.
(v) The authors  achieved the values of derivative parameters by solving the three systems of linear equations, which is computationally expensive as compared to methods developed in this paper where there exists only one tridiagonal system of linear equations for finding the values of derivative parameters.
Further, V[N x N] and H[N x N] are the tridiagonal matrices obtained from [V.sub.i] and [h.sub.i] elements by using rules defined in .
find the n x n, real, symmetric, and tridiagonal matrix, B, such that [lambda](B) = [([[lambda].sub.i]).sup.n.sub.1] are the eigenvalues of [lambda], while [lambda]([B.sup.o]) = [([[lambda].sup.o.sub.i]).sup.n-1.sub.1] 1 are the eigenvalues of the leading principal submatrix of B, where [B.sup.o] is obtained from B by deleting the last row and column.
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