writer
6,694
edits
Changes
Jump to navigation
Jump to search
Line 1:
Line 1: − + + + + + + + + + + + + + + + + + + +
no edit summary
<div style="font-size:30px">'''TRIDIAGONAL'''</div><br/>
<div style="font-size:30px">'''MATRIX("TRIDIAGONAL",order)'''</div><br/>
*<math>order</math> is the size of the Tridiagonal matrix.
==Description==
*This function returns the matrix with the property of tridiagonal.
*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.
*So a tridiagonal matrix is a matrix that has nonzero elements only on the main diagonal, the first diagonal below this, and the first diagonal above the main diagonal.
*A tridiagonal is of the form:
<math>\begin{vmatrix}
a_{11} & a_{12} & 0 & 0 & \cdots & 0 & 0 \\
a_{21} & a_{22} & a_{23} & \cdots & 0 & 0 \\
0 & a_{32} & a_{33} & \ddots & a_{n-2,n-1} & 0 \\
\vdots &\ddots & \ddots & \ddots & a_{n-1,n-1} & a_{n-1,n}
0 & 0 & \cdots &\cdots & a_{n,n-1} & a_{nn}
\end{vmatrix}</math>
*A general tridiagonal matrix is not necessarily symmetric or Hermitian,but tridiagonal matrix is a matrix that is both upper and lower Hessenberg matrix.
*In Calci, MATRIX("tridiagonal") gives the tridiagonal matirx of order 3.
*Users can change the order of the matrix.