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.