This Hasse diagram explicitly handles the field dependency of matrix properties. Many relationships depend on whether matrices are over the real field ℝ or complex field ℂ.
Key Distinctions: • Over ℝ: Hermitian ≡ Symmetric, Unitary ≡ Orthogonal, Skew-Hermitian ≡ Skew-Symmetric • Over ℂ: These are distinct properties with different inclusion relationships • Universal: Properties like Square, Triangular, Diagonal hold over any field • Special Cases: Zero and Identity have universal properties but field-specific characterizations
Use the field selector to explore how relationships change between real and complex contexts. This reveals the deep mathematical structure and avoids common misconceptions about matrix properties.