# characteristic polynomial

## EnglishEdit

### NounEdit

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

#### Usage notesEdit

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.