Definition:Characteristic Matrix/Also defined as

Characteristic Matrix: Also defined as

Some sources define the characteristic matrix of $\mathbf A$ over $R \sqbrk x$ as:

$\mathbf A - x \mathbf I_n$

where:

$R$ is a commutative ring with unity.

$\mathbf A$ is a square matrix over $R$ of order $n > 0$.

$\mathbf I_n$ is the $n \times n$ identity matrix.

$R \sqbrk x$ is the polynomial ring in one variable over $R$.

Also see

• Results about characteristic matrices can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): characteristic matrix