# Notes - Linear Algebra II HT23, Permutations

### Flashcards

What is the definition of a permutation of $\{1, \ldots, n\}$?

A bijection $\sigma$ from $\{1, \ldots, n\}$ to itself.

What is the definition of a transposition of $\{1, \ldots, n\}$?

A permutation that fixes all but $2$ elements.

What is the sign/parity $\text{sgn}$ of a a permutation $\sigma$?

\[(-1)^k\]

where $k$ is the minimum number of transpositions.