Mathlib Map

Theorems · Theorem · linear algebra

Matrix.transpose_hasOrthogonalRows_iff_hasOrthogonalCols

∀ {α : Type u_1} {n : Type u_2} {m : Type u_3} [inst : Mul α] [inst_1 : AddCommMonoid α] (A : Matrix m n α)
  [inst_2 : Fintype m], A.transpose.HasOrthogonalRows ↔ A.HasOrthogonalCols

Aᵀ has orthogonal rows iff A has orthogonal columns.

Defined in
Mathlib.LinearAlgebra.Matrix.Orthogonal
Cited by
0 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
MulAddCommMonoidFintype
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AddCommMonoid · cited by 12281AddCommMonoidFintype · cited by 7736FintypeMatrix · cited by 4303MatrixMatrix.transpose · cited by 389Matrix.transposeMatrix.HasOrthogonalCols · cited by 7Matrix.HasOrthogonalColsMatrix.HasOrthogonalRows · cited by 7Matrix.HasOrthogonalRowsMatrix.transpose_hasOrthogona…CITED BYCITES

Cites6

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

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.