# characteristic polynomial

## English

### Noun

1. (linear algebra) The polynomial produced from a given square matrix by first subtracting the appropriate identity matrix multiplied by an indeterminant and then calculating the determinant.
The characteristic polynomial of ${\displaystyle \textstyle \left({\begin{array}{cc}1&4\\3&-5\end{array}}\right)}$ is ${\displaystyle \textstyle \left\vert {\begin{array}{cc}1-x&4\\3&-5-x\end{array}}\right\vert =x^{2}+4x-17}$.

#### Usage notes

Equally many authors instead subtract the matrix from the indeterminant times the identity matrix. The result differs only by a factor of -1, which turns out to be unimportant in the theory of characteristic polynomials.