inner_vsub_vsub_left_eq_dist_sq_right_iff

English

For a linear map f: E →ₗ[𝕜] E and ONB v₁, the (i,j)-entry of the matrix [f]_{v₁} is the inner product ⟪v₁ i, f(v₁ j)⟫.

Русский

Для отображения f: E →ₗ[𝕜] E и ONB v₁ элемент матрицы [f]_{v₁} в позиции (i,j) равен скалярному произведению ⟪v₁ i, f(v₁ j)⟫.

LaTeX

$$$[f]_{v_1}(i,j) = \langle v_1 i, f(v_1 j)\rangle$$$

Lean4

theorem inner_vsub_vsub_left_eq_dist_sq_right_iff {a b c : P} :
    ⟪a -ᵥ b, a -ᵥ c⟫ = dist a c ^ 2 ↔ ⟪c -ᵥ b, a -ᵥ c⟫ = 0 := by
  rw [real_inner_comm, inner_vsub_vsub_left_eq_dist_sq_left_iff, real_inner_comm]

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