Nilpotent maps on finite modules #
theorem
Module.End.isNilpotent_iff_of_finite
{R : Type u_1}
{M : Type u_2}
[CommSemiring R]
[AddCommMonoid M]
[Module R M]
[Module.Finite R M]
{f : End R M}
:
@[simp]
theorem
Matrix.isNilpotent_transpose_iff
{R : Type u_1}
[CommSemiring R]
{ι : Type u_3}
[DecidableEq ι]
[Fintype ι]
{A : Matrix ι ι R}
:
theorem
Matrix.isNilpotent_iff
{R : Type u_1}
[CommSemiring R]
{ι : Type u_3}
[DecidableEq ι]
[Fintype ι]
{A : Matrix ι ι R}
:
theorem
Matrix.isNilpotent_iff_forall_row
{R : Type u_1}
[CommSemiring R]
{ι : Type u_3}
[DecidableEq ι]
[Fintype ι]
{A : Matrix ι ι R}
:
theorem
Matrix.isNilpotent_iff_forall_col
{R : Type u_1}
[CommSemiring R]
{ι : Type u_3}
[DecidableEq ι]
[Fintype ι]
{A : Matrix ι ι R}
: