`MatrixBridge`

definition

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module: IndisputableMonolith.Relativity.Geometry.MatrixBridge
domain: Relativity
line: 19 · github
papers citing: none yet

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IndisputableMonolith.Relativity.Geometry.MatrixBridge on GitHub at line 19.

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formal source

  16namespace Geometry
  17
  18/-- **SCAFFOLD**: Minimal placeholder for the matrix bridge infrastructure. -/
  19structure MatrixBridge where
  20  matrix : Matrix (Fin 4) (Fin 4) ℝ := 1
  21
  22/-- The Minkowski metric matrix $\eta_{\mu\nu} = \text{diag}(-1, 1, 1, 1)$. -/
  23noncomputable def minkowskiMatrix : Matrix (Fin 4) (Fin 4) ℝ :=
  24  Matrix.diagonal fun i => if i.val = 0 then -1 else 1
  25
  26/-- Bridge is accepted if the matrix is invertible (non-zero determinant). -/
  27def MatrixBridgeAccepts (B : MatrixBridge) : Prop :=
  28  B.matrix.det ≠ 0
  29
  30@[simp] lemma matrixBridge_accepts_identity : MatrixBridgeAccepts {} := by
  31  unfold MatrixBridgeAccepts
  32  simp [MatrixBridge]
  33
  34
  35end Geometry
  36end Relativity
  37end IndisputableMonolith

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