Definition:Jordan Matrix

Definition

A Jordan matrix is a square matrix in which:

the diagonal elements are all non-zero and equal

the elements on the first superdiagonal are all equal to $1$

all other elements are zero.

Examples

Arbitrary Example

This is an arbitrary example of an order $4$ Jordan matrix:

$\quad \begin {pmatrix} \lambda & 1 & 0 & 0 \\ 0 & \lambda & 1 & 0 \\ 0 & 0 & \lambda & 1 \\ 0 & 0 & 0 & \lambda \end {pmatrix}$

where it is understood that $\lambda \ne 0$.

Also see

• Results about Jordan matrices can be found here.

Source of Name

This entry was named for Marie Ennemond Camille Jordan.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Jordan matrix
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Jordan matrix