Assertion: matrix's determinant | /r/HasProperty | unchanged
Facets:
value: upon replacing one row
type: TEMPORAL
value: under transposition of the matrix
type: OTHER
Source sentences:
text: A meaning can be given to the Leibniz formula provided that the order for the product is specified, and similarly for other definitions of the determinant, but non-commutativity then leads to the loss of many fundamental properties of the determinant, such as the multiplicative property or the fact that the determinant is unchanged under transposition of the matrix.
text: And the determinant of M in any dimension is linear in each of its rows or columns and is unchanged upon replacing one row , say q, by the sum of q and any multiple of any other row.