Theorems · Theorem · linear algebra

Matrix.det_toBlock

∀ {m : Type u_3} {R : Type v} [inst : CommRing R] [inst_1 : DecidableEq m] [inst_2 : Fintype m] (M : Matrix m m R)
  (p : m → Prop) [inst_3 : DecidablePred p],
  M.det =
    (Matrix.fromBlocks (M.toBlock p p) (M.toBlock p fun j => ¬p j) (M.toBlock (fun j => ¬p j) p)
        (M.toBlock (fun j => ¬p j) fun j => ¬p j)).det

Defined in

Mathlib.LinearAlgebra.Matrix.Block

Cited by

1 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingDecidableEqFintypeDecidablePred