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Glite Dictionary
🟦 Matrix equals negative transpose 🔄 Changes sign when swapped ↔️ Only equal if reversed
antisymmetric

antisymmetric

1 8.6
A square grid of numbers that becomes its negative when rows and columns swap, so diagonal numbers are zero
  • adjective
  • /ˌæntiˈsɪmɛtrɪk/
  • Specialized
: antisimétrico
  • In linear algebra, an antisymmetric matrix is defined as one where A = -A^T, where A^T is the transpose of A.

Here is a combination, not symmetric, not antisymmetric, but still a good matrix.

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Examples

  • An antisymmetric matrix has all diagonal entries equal to zero, meaning it is equal to the negative of its transpose.

  • What do you think you know about the eigenvalues for antisymmetric matrices?

    MIT OpenCourseWare

  • To understand the properties of antisymmetric matrices, note that their eigenvalues are purely imaginary.

Surface Forms

antisymmetric positive

Morphology

antisymmetric = symmetric (semi-transparent) = anti + symmetr + ic

This is a standard technical use of anti- + symmetric, but the matrix property and zero-diagonal consequence are not directly guessable from the parts alone.

Etymology

Antisymmetric comes from the parts anti- 'against' and symmetric 'same on both sides'. Think of a mirror image that is also inverted: flipping a matrix (taking its transpose) gives the negative, which is why all diagonal entries must be zero.