Definition:Jordan Matrix
Jump to navigation
Jump to search
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