Assertion: determinant's number | /r/HasProperty | odd
Facets:
Source sentences:
text: 2 mathematics : a square array of numbers bordered on the left and right by a vertical line and having a value equal to the algebraic sum of all possible products where the number of factors in each product is the same as the number of rows or columns, each factor in a given product is taken from a different row and column, and the sign of a product is positive or negative depending upon whether the number of permutations necessary to place the indices representing each factor's position in its row or column in the order of the natural numbers is odd or even
text: If the number of transpositions that define a permutation is odd, then the permutation is said to be odd, and its sign is −1.
text: One or minus one, depending whether the number of exchanges was even or the number of exchanges was odd.
text: One or minus one, depending whether the number of exchanges was even or the number of exchanges was odd.
text: The number of transpositions determines the parity of the permutation (even if the number of transpositions is even, and odd otherwise).