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Glite Dictionary
📊 Not standard 🔢 Not commuting 🧩 Not invariant
non-normal

non-normal

9.9
A matrix or operator whose eigenvectors may not be perpendicular
  • adjective
  • /nɒnˈnɔːrməl/
  • Specialized
translation icon : no normal
  • Because the operator is non-normal, its eigenvectors are not guaranteed to be orthogonal.

Examples

  • The non-normal matrix presented unique challenges in the spectral analysis.

  • Researchers often encounter non-normal operators when studying complex systems in physics.

  • This matrix is non-normal.

  • The operator is non-normal!

  • The non-normal matrix caused difficulties in finding the eigenvalues, as they were not orthogonal.

  • In linear algebra, a non-normal operator often leads to eigenvectors that are not orthogonal to each other.

  • Students studying linear algebra should understand that non-normal matrices can complicate eigenvector calculations.

Surface Forms

non-normal positive

Morphology

non-normal = normal (semi-transparent) = non + normal

Morphologically transparent (non- + normal) but the technical linear-algebra sense of 'normal' (commuting with its adjoint) is specialized jargon that a general learner may not know.

Etymology

Non-normal comes from non- ('not') and normal, where normal once meant a rule or a builder's 'square' that makes things 'line up'. In linear algebra a non-normal operator does not 'line up' with its matching partner, which is why its special directions may not meet at 'right angles'.