Theorems · Definition · linear algebra
Matrix.BlockTriangular
{α : Type u_1} → {m : Type u_3} → {R : Type v} → [LT α] → [Zero R] → Matrix m m R → (m → α) → PropLet b map rows and columns of a square matrix M to blocks indexed by αs. Then
BlockTriangular M n b says the matrix is block triangular.
- Defined in
- Mathlib.LinearAlgebra.Matrix.Block
- Cited by
- 45 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
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
Cited by49
Results whose statement or proof uses this declaration.
- Matrix.IsUpperTriangularproof · cited by 8
- Matrix.IsLowerTriangularproof · cited by 7
- Matrix.BlockTriangular.addstatement and proof · cited by 6
- Matrix.blockTriangular_diagonalstatement · cited by 3
- Matrix.BlockTriangular.detstatement and proof · cited by 3
- Matrix.BlockTriangular.substatement and proof · cited by 3
- Matrix.BlockTriangular.submatrixstatement and proof · cited by 3
- isClosed_setOfPred_blockTriangularstatement · cited by 2
- Matrix.blockTriangularSubsemiringproof · cited by 2
- Matrix.blockTriangular_onestatement · cited by 2
- Matrix.blockTriangular_singlestatement · cited by 2
- Algebra.Norm.Transitivity.auxMat_blockTriangularstatement · cited by 2