Theorems · Theorem · linear algebra
Matrix.mul_diagonal
∀ {m : Type u_2} {n : Type u_3} {α : Type v} [inst : NonUnitalNonAssocSemiring α] [inst_1 : Fintype n]
[inst_2 : DecidableEq n] (d : n → α) (M : Matrix m n α) (i : m) (j : n), (M * Matrix.diagonal d) i j = M i j * d j- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Matrix.diagonalstatement · cited by 314
- Matrix.diagonal_transposeproof · cited by 17
- dotProduct_diagonalproof · cited by 1
Cited by15
Results whose statement or proof uses this declaration.
- Matrix.mul_oneproof · cited by 45
- Matrix.diagonal_mul_diagonalproof · cited by 9
- Matrix.center_eq_scalar_imageproof · cited by 6
- Matrix.smul_eq_mul_diagonalproof · cited by 3
- RootPairing.Base.cartanMatrixIn_mul_diagonal_eqproof · cited by 2
- RootPairing.Base.cartanMatrix_mul_diagonal_eqproof · cited by 1
- Matrix.commutator_diag2_transvectionproof · cited by 1
- Matrix.transvection_mem_commutator₁proof · cited by 1
- Matrix.SpecialLinearGroup.toGL_mem_center_iffproof · cited by 0
- Matrix.dotProduct_vecMul_hadamardproof · cited by 0
- LieAlgebra.Orthogonal.indefiniteDiagonal_transformproof · cited by 0
- Matrix.exists_rank_normal_formproof · cited by 0