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Theorems · Theorem · linear algebra

Matrix.BlockTriangular.charmatrix

∀ {R : Type u_1} [inst : CommRing R] {n : Type u_4} [inst_1 : DecidableEq n] [inst_2 : Fintype n] {α : Type u_5}
  [inst_3 : Preorder α] {M : Matrix n n R} {b : n → α}, M.BlockTriangular b → M.charmatrix.BlockTriangular b

Alias of the reverse direction of Matrix.charmatrix_blockTriangular_iff.

Defined in
Mathlib.LinearAlgebra.Matrix.Charpoly.Basic
Cited by
2 results in Mathlib
Foundations
Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingDecidableEqFintypePreorder
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Around this declaration

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

Matrix.charpoly_of_isUpperTriangular · cited by 1Matrix.charpoly_of_isUppe…Matrix.BlockTriangular.charpoly · cited by 0BlockTriangular.charpolyCommRing · cited by 17173CommRingPreorder · cited by 7952PreorderFintype · cited by 7736FintypePolynomial · cited by 5681PolynomialMatrix · cited by 4303MatrixMatrix.BlockTriangular · cited by 45Matrix.BlockTriangularMatrix.charmatrix · cited by 42Matrix.charmatrixMatrix.charmatrix_blockTriangular_iff · cited by 2Matrix.charmatrix_blockTr…BlockTriangular.charmatrixCITED BYCITES

Cites8

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

Cited by2

Results whose statement or proof uses this declaration.