Definition:Characteristic Matrix

Definition

Let $R$ be a commutative ring with unity.

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

Let $\mathbf I_n$ be the $n \times n$ identity matrix.

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

The characteristic matrix of $\mathbf A$ over $R \sqbrk x$ is the square matrix:

$\mathbf I_n x - \mathbf A$

Also defined as

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

$\mathbf A - x \mathbf I_n$

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