Assertion: determinant | /r/HasProperty | unique number
Facets:
value: from n × n matrices
type: OTHER
value: in other words
type: OTHER
Source sentences:
text: The determinant is a unique number associated with each square matrix and is obtained after performing a certain calculation for the elements in the matrix.
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).
text: A matrix is a group of numbers, and a determinant is a unique number related to that matrix.
text: In this definition of the determinant, all the work that would normally go into showing that the determinant is the unique function with such-and-such properties goes into showing that $\Lambda^n(V)$ is one-dimensional.