Theorems · Theorem · linear algebra

Module.Basis.matrix_apply

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {m : Type u_4} {n : Type u_5} [inst : Fintype m] [inst_1 : Fintype n]
  [inst_2 : Semiring R] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] (b : Module.Basis ι R M) (i : m) (j : n)
  (k : ι) [inst_5 : DecidableEq m] [inst_6 : DecidableEq n],
  (Module.Basis.matrix m n b) (i, j, k) = Matrix.single i j (b k)

Defined in: Mathlib.LinearAlgebra.Matrix.StdBasis
Cited by: 0 results in Mathlib
Foundations: Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype Fintype Semiring AddCommMonoid Module DecidableEq DecidableEq

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DFunLike.coestatement and proof · cited by 62,936
Modulestatement and proof · cited by 20,661
Semiringstatement and proof · cited by 13,802
AddCommMonoidstatement and proof · cited by 12,281
Fintypestatement and proof · cited by 7,736
Matrixstatement · cited by 4,303
Equiv.symmproof · cited by 3,681
Module.Basisstatement and proof · cited by 1,477
Pi.singleproof · cited by 518
Equiv.transproof · cited by 337
Matrix.ofproof · cited by 336
Equiv.reflproof · cited by 274

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