# characteristic polynomial

## English

### Noun

1. (linear algebra) The determinant, of a matrix minus an indeterminant times the identity matrix
The characteristic polynomial of $\left(\begin{array}{cc}1 & 4\\3 & -5\end{array}\right)$ is $\mathbf{Det}\left(\begin{array}{cc}1-x & 4\\ 3 & -5-x\end{array}\right)$.

#### Usage notes

Equally many authors instead subtract the matrix from the indeterminant times the identity matrix. But the result only differs by multiplication by -1, which isn't important where characteristic polynomials are studied.