Assertion: determinant | /r/HasProperty | linear
Facets:
value: in columns
type: LOCATION
value: in the j-th column
type: TEMPORAL
value: in each row
type: LOCATION
value: independently
type: MANNER
Source sentences:
text: , the determinant is linear in the remaining column, that is
text: Multilinearity means that the determinant is a linear function in each column of the input matrix, independently.
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: The determinant of a matrix is linear in each row.
text: The determinant is linear in the rows and columns of the matrix.
text: (Also since the determinant is linear in the j-th column this term can have no factor other than m ij from that column.)
text: The determinant is a linear function.