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formal statement (Lean)
56theorem hpOperator_isSymm (q : ℕ) (a : ℤ) :
57 (hpOperator q a).IsSymm := by
proof body
Term-mode proof.
58 unfold hpOperator Matrix.IsSymm
59 ext i j
60 fin_cases i <;> fin_cases j <;> rfl
61
62/-! ## Eigenvalues
63
64The characteristic polynomial of `[[0, θ], [θ, 0]]` is `λ² - θ²`, with
65roots `±θ`. We exhibit eigenvectors directly. -/
66
67/-- The vector `(1, 1)` is an eigenvector with eigenvalue `+θ`. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (10)
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