Theorems · Theorem · linear algebra

Matrix.IsHermitian.eigenvalues_eq_zero_iff

∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {n : Type u_2} [inst_1 : Fintype n] {A : Matrix n n 𝕜} [inst_2 : DecidableEq n]
  (hA : A.IsHermitian), hA.eigenvalues = 0 ↔ A = 0

The eigenvalues of a Hermitian matrix A are all zero iff A = 0.

Defined in

Mathlib.Analysis.Matrix.Spectrum

Cited by

1 results in Mathlib

Foundations

Depth 262 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeFintypeDecidableEq