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Glite Dictionary
🕵️ Leaving no sign 🔢 Zero trace
traceless

traceless

9.4
In math, having the sum of the numbers on its diagonal equal to zero
  • adjective
  • /ˈtreɪsləs/
  • Specialized
translation icon : sin traza
  • The transformation is traceless, meaning the sum of its diagonal elements is zero.

Examples

  • A traceless matrix is important in certain areas of quantum mechanics.

  • A traceless matrix can simplify calculations in linear algebra.

  • Physicists often work with traceless operators when studying symmetry properties.

  • Is the function traceless when evaluated at these points?

  • In quantum mechanics, a traceless matrix is crucial because its diagonal elements sum to zero.

  • A common property of traceless operators is that they help maintain symmetry in physical equations.

  • When dealing with quantum states, it is often required that the transformation remains traceless.

Surface Forms

traceless positive

Morphology

traceless = trace (semi-transparent) = trace + less

The form is still clearly 'trace' + '-less', but the mathematical sense depends on the technical meaning of 'trace' rather than the everyday one.

Etymology

Traceless in math comes from trace, which here means 'the sum of the numbers on the main diagonal' of a square table of numbers, and -less means 'without'. So a traceless matrix is like it 'leaves no mark' because the diagonal numbers add up to zero.