Assertion: matrix's determinant | /r/HasProperty | unique function
Facets:
value: in other words
type: OTHER
value: from n × n matrices
type: OTHER
Source sentences:
text: Properties 1, 8 and 10 — which all follow from the Leibniz formula — completely characterize the determinant; in other words the determinant is the unique function from n × n matrices to scalars that is n-linear alternating in the columns, and takes the value 1 for the identity matrix (this characterization holds even if scalars are taken in any given commutative ring).