Theorems · Definition · linear algebra
Matrix.HasOrthogonalRows
{α : Type u_1} → {n : Type u_2} → {m : Type u_3} → [Mul α] → [AddCommMonoid α] → Matrix m n α → [Fintype n] → PropA.HasOrthogonalRows means matrix A has orthogonal rows (with respect to
dotProduct).
- Defined in
- Mathlib.LinearAlgebra.Matrix.Orthogonal
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- Assumes
- MulAddCommMonoidFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- dotProductproof · cited by 194
Cited by8
Results whose statement or proof uses this declaration.
- Matrix.HasOrthogonalColsproof · cited by 7
- Matrix.HasOrthogonalCols.hasOrthogonalRowsstatement · cited by 0
- Matrix.HasOrthogonalCols.transpose_hasOrthogonalRowsstatement · cited by 0
- Matrix.HasOrthogonalRows.hasOrthogonalColsstatement and proof · cited by 0
- Matrix.HasOrthogonalRows.transpose_hasOrthogonalColsstatement and proof · cited by 0
- Matrix.transpose_hasOrthogonalCols_iff_hasOrthogonalRowsstatement · cited by 0
- Matrix.mul_transpose_self_isDiag_iff_hasOrthogonalRowsstatement · cited by 0
- Matrix.transpose_hasOrthogonalRows_iff_hasOrthogonalColsstatement · cited by 0