Category:Definitions/Characteristic Polynomial of Matrix

This category contains definitions related to Characteristic Polynomial of Matrix.
Related results can be found in Category:Characteristic Polynomial of Matrix.

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 polynomial of $\mathbf A$ is the determinant of the characteristic matrix of $\mathbf A$ over $R \sqbrk x$:

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