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Theorems · Definition · linear algebra

Matrix.swap

(R : Type u_1) → {n : Type u_2} → [Zero R] → [One R] → [DecidableEq n] → n → n → Matrix n n R

The swap matrix swap R i j is the identity matrix with the i-th and j-th rows modified such that multiplying by it on the left (resp. right) corresponds to swapping the i-th and j-th row (resp. column).

Defined in
Mathlib.LinearAlgebra.Matrix.Swap
Cited by
19 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
ZeroOneDecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Matrix.GeneralLinearGroup.swap · cited by 2GeneralLinearGroup.swapMatrix.swap_comm · cited by 2Matrix.swap_commMatrix.transpose_swap · cited by 1Matrix.transpose_swapMatrix.map_swap · cited by 1Matrix.map_swapMatrix.mul_swap_apply_left · cited by 1Matrix.mul_swap_apply_leftMatrix.swap_mul_apply_left · cited by 1Matrix.swap_mul_apply_leftMatrix.GeneralLinearGroup.map_swap · cited by 0GeneralLinearGroup.map_sw…Matrix.conjTranspose_swap · cited by 0Matrix.conjTranspose_swapMatrix.GeneralLinearGroup.val_swap · cited by 0GeneralLinearGroup.val_sw…Matrix.mul_swap_apply_right · cited by 0Matrix.mul_swap_apply_rig…Matrix.mul_swap_of_ne · cited by 0Matrix.mul_swap_of_neMatrix.swap.congr_simp · cited by 0swap.congr_simpMatrix.swap_mulVec · cited by 0Matrix.swap_mulVecMatrix.swap_mulVec_apply · cited by 0Matrix.swap_mulVec_applyMatrix.swap_mul_apply_right · cited by 0Matrix.swap_mul_apply_rig…Matrix · cited by 4303MatrixEquiv.swap · cited by 197Equiv.swapEquiv.Perm.permMatrix · cited by 25Perm.permMatrixMatrix.swapCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by20

Results whose statement or proof uses this declaration.