Band matrix Totally Explained

Everything about Band Matrix totally explained

In mathematics, particularly matrix theory, a band matrix is a sparse matrix, whose non-zero entries are confined to a diagonal band, comprising the main diagonal and zero or more diagonals on either side. Formally, an n×n matrix A=(a_i,j) is a band matrix if all matrix elements are zero outside a diagonally bordered band whose range is determined by constants k₁ and k₂: ť

a_

Examples and special cases

The following are special cases of band matrices:

Diagonal matrices.
Tridiagonal matrices.
Pentadiagonal matrices.
Upper and lower triangular matrices.
Upper and lower Hessenberg matrices.
Block-diagonal matrices.
Shift matrices and shear matrices.
Matrices in Jordan normal form.
A skyline matrix is a more compact way of storing a banded matrix.

The inverses of Lehmer matrices are constant tridiagonal matrices, and are thus band matrices.

Further Information

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