Theorems · Definition · linear algebra
Matrix.HasOrthogonalCols
{α : Type u_1} → {n : Type u_2} → {m : Type u_3} → [Mul α] → [AddCommMonoid α] → Matrix m n α → [Fintype m] → PropA.HasOrthogonalCols means matrix A has orthogonal columns (with respect to
dotProduct).
- Defined in
- Mathlib.LinearAlgebra.Matrix.Orthogonal
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- MulAddCommMonoidFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Matrix.transposeproof · cited by 389
- Matrix.HasOrthogonalRowsproof · cited by 7
Cited by7
Results whose statement or proof uses this declaration.
- Matrix.transpose_mul_self_isDiag_iff_hasOrthogonalColsstatement · cited by 0
- Matrix.HasOrthogonalCols.hasOrthogonalRowsstatement and proof · cited by 0
- Matrix.HasOrthogonalCols.transpose_hasOrthogonalRowsstatement and proof · cited by 0
- Matrix.HasOrthogonalRows.hasOrthogonalColsstatement · cited by 0
- Matrix.HasOrthogonalRows.transpose_hasOrthogonalColsstatement · cited by 0
- Matrix.transpose_hasOrthogonalCols_iff_hasOrthogonalRowsstatement · cited by 0
- Matrix.transpose_hasOrthogonalRows_iff_hasOrthogonalColsstatement · cited by 0