Theorems · Theorem · linear algebra
Matrix.submatrix_mul_equiv
∀ {l : Type u_1} {m : Type u_2} {n : Type u_3} {o : Type u_4} {α : Type v} [inst : Fintype n] [inst_1 : Fintype o]
[inst_2 : AddCommMonoid α] [inst_3 : Mul α] {p : Type u_10} {q : Type u_11} (M : Matrix m n α) (N : Matrix n p α)
(e₁ : l → m) (e₂ : o ≃ n) (e₃ : q → p), M.submatrix e₁ ⇑e₂ * N.submatrix (⇑e₂) e₃ = (M * N).submatrix e₁ e₃- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- Equivstatement and proof · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Matrix.submatrixstatement · cited by 183
- Equiv.bijectiveproof · cited by 132
- Matrix.submatrix_mulproof · cited by 1
Cited by11
Results whose statement or proof uses this declaration.
- LinearMap.charpoly_toMatrixproof · cited by 9
- Matrix.mul_eq_one_comm_of_equivproof · cited by 4
- Matrix.det_comm'proof · cited by 3
- Matrix.mem_subfield_of_mul_eq_one_of_mem_subfield_rightproof · cited by 1
- Matrix.IsHadamard.reindexproof · cited by 1
- Matrix.submatrix_mul_transpose_submatrixproof · cited by 1
- Matrix.mul_submatrix_oneproof · cited by 1
- Matrix.reindexLinearEquiv_mulproof · cited by 1
- Matrix.TransvectionStruct.toMatrix_reindexEquiv_prodproof · cited by 1
- Matrix.fromBlocks_eq_of_invertible₂₂proof · cited by 0
- Matrix.one_submatrix_mulproof · cited by 0