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Theorems · Theorem · linear algebra

Matrix.smul_eq_diagonal_mul

∀ {m : Type u_2} {n : Type u_3} {α : Type v} [inst : NonUnitalNonAssocSemiring α] [inst_1 : Fintype m]
  [inst_2 : DecidableEq m] (M : Matrix m n α) (a : α), a • M = (Matrix.diagonal fun x => a) * M
Defined in
Mathlib.Data.Matrix.Mul
Cited by
6 results in Mathlib
Foundations
Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonUnitalNonAssocSemiringFintypeDecidableEq
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.det_smul · cited by 11Matrix.det_smulMatrix.reverse_charpoly · cited by 3Matrix.reverse_charpolyLinearMap.toMatrix_algebraMap · cited by 2LinearMap.toMatrix_algebr…MatrixModCat.isScalarTower_toModuleCat · cited by 2MatrixModCat.isScalarTowe…LinearMap.toMatrix'_algebraMap · cited by 1LinearMap.toMatrix'_algeb…Matrix.charpoly_inv · cited by 0Matrix.charpoly_invFintype · cited by 7736FintypeMatrix · cited by 4303MatrixNonUnitalNonAssocSemiring · cited by 1081NonUnitalNonAssocSemiringMatrix.ext · cited by 540Matrix.extMatrix.diagonal · cited by 314Matrix.diagonalMatrix.diagonal_mul · cited by 5Matrix.diagonal_mulMatrix.smul_eq_diagonal_mulCITED BYCITES

Cites6

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Cited by6

Results whose statement or proof uses this declaration.