IsSkewHermitian

Tests if a matrix is skew-Hermitian.

Syntax

• IsSkewHermitian(A[, ε])

  • A is a matrix

  • ε is a positive number

Description

If A is a matrix, then IsSkewHermitian(A) returns true iff A is skew-Hermitian, that is, iff A is square and A[i, j] = −A[j, i]* for all valid indices i and j. (Here, the asterisk denotes complex conjugation of a complex number.) Floating-point comparisons are made with epsilon ε.

Examples

A ≔ ❨❨0, 2, 1, 1❩, ❨−2, 0, −1, 2❩, ❨−1, 1, 0, −2❩, ❨−1, −2, 2, 2⋅i❩❩

⎛  0    2    1    1⎞
⎜ −2    0   −1    2⎟
⎜ −1    1    0   −2⎟
⎝ −1   −2    2  2⋅i⎠

IsSkewHermitian(A)

true

See also

• IsHermitian

• IsSkewSymmetric