Assertion: determinant | /r/HasProperty | unchanged
Facets:
value: by these actions
type: OTHER
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: A more familiar property of a determinant is that if you add a multiple of a row (or column) to a different row (or column) of a square matrix then its determinant is unchanged.
text: The sign of the determinant changes, but the matrix is unchanged and so its determinant is unchanged.
text: The determinant (which is unchanged by these actions) is then the product of the diagonal entries.