linear algebra Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matric ...

, a pentadiagonal matrix is a special case of band matrices. Its only nonzero entries are on the main diagonal and the first two upper and two lower diagonals. So, it is of the form. :

\begin 
   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_ & 0 \\
   \vdots & \ddots & \ddots & \ddots & \ddots & d_ & e_ \\
   \vdots & & \ddots & a_ & b_ & c_ & d_ \\
   0 & \cdots & \cdots & 0 & a_ & b_ & c_n 
\end
\in\; \R^
\,.

It follows that a pentadiagonal matrix has at most

5n-6

nonzero entries, where ''n'' is the size of the

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. Hence, pentadiagonal matrices are

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, making them useful in

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See also