IsLowerHessenberg

Tests if a matrix is lower Hessenberg.

Syntax

• IsLowerHessenberg(A[, ε])

  • A is a matrix

  • ε is a positive number

Description

If A is a matrix, not necessarily square, then IsLowerHessenberg(A, ε) is true iff i < j − 1 implies A[i, j] = 0 (with epsilon ε).

Examples

A ≔ ❨❨1, 3, 0, 0, 0❩, ❨5, 6, 3, 0, 0❩, ❨4, 0, 2, 1, 0❩, ❨5, 6, 3, 2, 1❩, ❨1, 0, 2, 5, 3❩❩

⎛1  3  0  0  0⎞
⎜5  6  3  0  0⎟
⎜4  0  2  1  0⎟
⎜5  6  3  2  1⎟
⎝1  0  2  5  3⎠

IsLowerHessenberg(A)

true

See also

• IsUpperHessenberg

• IsLowerTriangular