A square matrix with nonzero elements only on the diagonal and slots horizontally or vertically adjacent the diagonal (i.e., along the subdiagonal and superdiagonal),
![[a_(11) a_(12) 0 0 ... 0 0; a_(21) a_(22) a_(23) ... ... 0 0; 0 a_(32) a_(33) ... ... a_(n-2,n-1) 0; | ... ... ... ... a_(n-1,n-1) a_(n-1,n); 0 0 ... ... ... a_(n,n-1) a_(nn)].](http://mathworld.wolfram.com/images/equations/TridiagonalMatrix/NumberedEquation1.svg) |
Computing the determinant of such a matrix requires only 
(as opposed to 
) arithmetic operations (Acton 1990, p. 332). Efficient solution of the matrix equation 
for 
, where 
is a tridiagonal matrix, can be performed in the Wolfram Language using LinearSolve on 
, represented as a SparseArray.
