pentadiagonal matrix

An $n\times n$ pentadiagonal matrix (with $n\geq 3$ ) is a matrix of the form

\begin{pmatrix}c_{1}&d_{1}&e_{1}&0&\cdots&\cdots&0\\ b_{1}&c_{2}&d_{2}&e_{2}&\ddots&&\vdots\\ a_{1}&b_{2}&\ddots&\ddots&\ddots&\ddots&\vdots\\ 0&a_{2}&\ddots&\ddots&\ddots&e_{n-3}&0\\ \vdots&\ddots&\ddots&\ddots&\ddots&d_{n-2}&e_{n-2}\\ \vdots&&\ddots&a_{n-3}&b_{n-2}&c_{n-1}&d_{n-1}\\ 0&\cdots&\cdots&0&a_{n-2}&b_{n-1}&c_{n}\end{pmatrix}.

It follows that a pentadiagonal matrix is determined by five vectors: one $n$ -vector $c=(c_{1},\ldots,c_{n})$ , two $(n-1)$ -vectors $b=(b_{1},\ldots,b_{n-1})$ and $d=(d_{1},\ldots,d_{n-1})$ , and two $(n-2)$ -vectors $a=(a_{1},\ldots,a_{n-2})$ and $e=(e_{1},\ldots,e_{n-2})$ . It follows that a pentadiagonal matrix is completely determined by $n+2(n-1)+2(n-2)=5n-6$ scalars.

Title	pentadiagonal matrix
Canonical name	PentadiagonalMatrix
Date of creation	2013-03-22 13:23:23
Last modified on	2013-03-22 13:23:23
Owner	drini (3)
Last modified by	drini (3)
Numerical id	6
Author	drini (3)
Entry type	Definition
Classification	msc 15-00
Classification	msc 65-00
Synonym	penta-diagonal matrix
Related topic	TridiagonalMatrix