Definition:Characteristic Polynomial of Matrix/Also defined as

Definition

Some sources define the characteristic polynomial of $\mathbf A$ as:

$\map {p_{\mathbf A} } x = \map \det {\mathbf A - x \mathbf I_n}$

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

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): characteristic polynomial