Theorems · Theorem · linear algebra
Matrix.mul_apply
∀ {l : Type u_1} {m : Type u_2} {n : Type u_3} {α : Type v} [inst : Fintype m] [inst_1 : Mul α]
[inst_2 : AddCommMonoid α] {M : Matrix l m α} {N : Matrix m n α} {i : l} {k : n}, (M * N) i k = ∑ j, M i j * N j k- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- FintypeMulAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- Finset.univstatement · cited by 3,473
Cited by16
Results whose statement or proof uses this declaration.
- Matrix.mul_adjugateproof · cited by 10
- UpperHalfPlane.denom_cocycleproof · cited by 2
- Matrix.isAddUnit_mulproof · cited by 2
- Algebra.traceMatrix_of_basis_mulVecproof · cited by 2
- Algebra.traceMatrix_of_matrix_vecMulproof · cited by 2
- SimpleGraph.mul_adjMatrix_applyproof · cited by 1
- SimpleGraph.incMatrix_mul_transpose_diagproof · cited by 1
- SimpleGraph.adjMatrix_mul_applyproof · cited by 1
- Ideal.single_mem_jacobson_matrixproof · cited by 1
- Matrix.pow_apply_nonnegproof · cited by 1
- Matrix.pow_apply_pos_iff_nonempty_pathproof · cited by 1
- UpperHalfPlane.mul_smul'proof · cited by 1