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Theorems · Definition · linear algebra

Matrix.TransvectionStruct.toMatrix

{n : Type u_1} → {R : Type u₂} → [DecidableEq n] → [CommRing R] → Matrix.TransvectionStruct n R → Matrix n n R

Associating to a transvection_struct the corresponding transvection matrix.

Defined in
Mathlib.LinearAlgebra.Matrix.Transvection
Cited by
32 results in Mathlib
Foundations
Depth 17 from the axioms · uses Quot.sound
Assumes
DecidableEqCommRing

Around this declaration

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

Matrix.TransvectionStruct.det · cited by 4TransvectionStruct.detMatrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvec · cited by 3Pivot.exists_list_transve…Matrix.TransvectionStruct.reverse_inv_prod_mul_prod · cited by 3TransvectionStruct.revers…Matrix.mem_range_scalar_of_commute_transvectionStruct · cited by 3Matrix.mem_range_scalar_o…Matrix.SpecialLinearGroup.scalar_eq_self_of_mem_center · cited by 2SpecialLinearGroup.scalar…Matrix.Pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal · cited by 2Pivot.reindex_exists_list…Matrix.TransvectionStruct.det_toMatrix_prod · cited by 2TransvectionStruct.det_to…Matrix.TransvectionStruct.inv_mul · cited by 2TransvectionStruct.inv_mulMatrix.TransvectionStruct.mul_inv · cited by 2TransvectionStruct.mul_invMatrix.TransvectionStruct.prod_mul_reverse_inv_prod · cited by 2TransvectionStruct.prod_m…Matrix.GeneralLinearGroup.mem_center_iff_val_mem_range_scalar · cited by 2GeneralLinearGroup.mem_ce…Matrix.TransvectionStruct.toMatrix_sumInl · cited by 2TransvectionStruct.toMatr…Real.map_matrix_volume_pi_eq_smul_volume_pi · cited by 1Real.map_matrix_volume_pi…Matrix.Pivot.exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec · cited by 1Pivot.exists_isTwoBlockDi…Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zero · cited by 1Pivot.exists_isTwoBlockDi…CommRing · cited by 17173CommRingMatrix · cited by 4303MatrixMatrix.TransvectionStruct · cited by 42Matrix.TransvectionStructMatrix.transvection · cited by 24Matrix.transvectionMatrix.TransvectionStruct.i · cited by 7TransvectionStruct.iMatrix.TransvectionStruct.j · cited by 6TransvectionStruct.jMatrix.TransvectionStruct.c · cited by 5TransvectionStruct.cTransvectionStruct.toMatrixCITED BYCITES

Cites7

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

Cited by32

Results whose statement or proof uses this declaration.