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.