Manuals/calci/TRIDIAGONAL

MATRIX("TRIDIAGONAL",order)

• $order$ 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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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}}

• 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.