English
There exists a determinant map on End_A(M) that is independent of the chosen basis: if M has a finite basis, det acts by det of the representing matrix; otherwise det is defined to be 1.
Русский
Существует базисно-независимаяDeterminant наEnd_A(M): если M имеет конечный базис,Det считаетDet отRepresenting matrix; иначеDet=fигр 1.
LaTeX
$$$\det: \mathrm{End}_A(M) \to A \\text{is such that }\det(f) = \det([f]_b)\text{ for any finite basis }b, \text{ and } \det(f) = 1\text{ if no finite basis exists.}$$$
Lean4
/-- The determinant of an endomorphism independent of basis.
If there is no finite basis on `M`, the result is `1` instead.
-/
def det :=
val_proj @wrapped✝.{}
