Assertion: determinant | /r/HasProperty | computed
Facets:
value: from scratch
type: MANNER
value: by writing down all permutations
type: MANNER
value: more easily
type: MANNER
Source sentences:
text: In linear algebra, the determinant is a scalar value that can be computed from the elements of a square matrix and encodes certain properties of the linear transformation described by the matrix.
text: Given a matrix A, some methods compute its determinant by writing A as a product of matrices whose determinants can be more easily computed.
text: If the determinant of A and the inverse of A have already been computed, the matrix determinant lemma allows rapid calculation of the determinant of A + uvT, where u and v are column vectors.
text: A determinant can also be computed by writing down all permutations of , taking each permutation as the subscripts of the letters , , ..., and summing with signs determined by , where is the number of permutation inversions in permutation (Muir 1960, p. 16), and is the permutation symbol.
text: The computation is relatively cheap because the determinant of A + uvT does not have to be computed from scratch (which in general is expensive).
text: The determinant of this matrix can be computed by using the Laplace expansion along any one of its rows or columns.
text: The determinant of this matrix can be computed by using the Laplace's cofactor expansion along the first two rows as follows.
text: Determinant in linear algebra is a useful value which is computed from the elements of a square matrix.