411 REFERENCE · Wikibooks
Linear Algebra/Definition of Determinant
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
Linear Algebra Definition of Determinant Determinants Exploration
For matrices, determining nonsingularity
is trivial.
is nonsingular iff
The formula came out in the course of developing
the inverse.
is nonsingular iff
The formula can be produced similarly
(see Problem 9).
is nonsingular iff
With these cases in mind, we posit a family of
formulas, , , etc.
determinantFor each the formula gives rise to a
determinant function
such that an matrix is nonsingular if and
only if .
(We usually omit the subscript because
if is then ""
could only mean "".)
Linear Algebra Definition of Determinant Determinants Exploration