Assertion: matrix's determinant | /r/HasProperty | linear
Facets:
value: by the sum
type: OTHER
value: in the remaining column
type: LOCATION
Source sentences:
text: , the determinant is linear in the remaining column, that is
text: Viewing an n × n matrix as being composed of n rows, the determinant is an n-linear function.
text: These equations say that the determinant is a linear function of each column, that interchanging adjacent columns reverses the sign of the determinant, and that the determinant of the identity matrix is 1.
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.