Theorems · Theorem · linear algebra
Matrix.transpose_transpose
∀ {m : Type u_2} {n : Type u_3} {α : Type v} (M : Matrix m n α), M.transpose.transpose = M- Defined in
- Mathlib.LinearAlgebra.Matrix.Defs
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Matrixstatement and proof · cited by 4,303
- Matrix.extproof · cited by 540
- Matrix.transposestatement and proof · cited by 389
Cited by34
Results whose statement or proof uses this declaration.
- Matrix.transposeAddEquivproof · cited by 11
- Matrix.adjugate_mulproof · cited by 6
- Matrix.det_succ_row_zeroproof · cited by 5
- Matrix.transpose_eq_diagonalproof · cited by 4
- SymplecticGroup.mem_iff'proof · cited by 2
- SymplecticGroup.transpose_memproof · cited by 2
- Matrix.cramer_eq_adjugate_mulVecproof · cited by 2
- Matrix.rank_submatrix_leproof · cited by 1
- Matrix.submatrix_succAbove_det_eq_negOnePow_submatrix_succAbove_det'proof · cited by 1
- Matrix.transpose_tsumproof · cited by 1
- Algebra.traceMatrix_of_matrix_mulVecproof · cited by 1
- LDL.diag_eq_lowerInv_conjproof · cited by 1