Definition:Characteristic Polynomial of Matrix/Also defined as
Jump to navigation
Jump to search
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