Theorems · Theorem · linear algebra
Matrix.updateCol_transpose
∀ {m : Type u_2} {n : Type u_3} {α : Type v} {M : Matrix m n α} {i : m} {b : n → α} [inst : DecidableEq m],
M.transpose.updateCol i b = (M.updateRow i b).transpose- Defined in
- Mathlib.LinearAlgebra.Matrix.RowCol
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Matrix.updateRowstatement and proof · cited by 63
- Matrix.updateColstatement and proof · cited by 45
- Matrix.transpose_applyproof · cited by 13
- Matrix.updateRow_applyproof · cited by 9
- Matrix.updateCol_applyproof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- Matrix.adjugate_applyproof · cited by 5
- Matrix.cramer_transpose_row_selfproof · cited by 2
- Matrix.updateCol_conjTransposeproof · cited by 0
- Matrix.cramer_transpose_applyproof · cited by 0
- Matrix.permanent_updateRow_smulproof · cited by 0