`issymmetric`

Tests whether a matrix is symmetric or skew-symmetric.

Syntax

tf = issymmetric(A)

True if A equals its transpose A.'.

tf = issymmetric(A, 'skew')

True if A equals -A.'.

tf = issymmetric(A, tol)

Accepts a relative difference up to tol.

Description

Symmetry refers to the plain transpose, not the conjugate transpose, so [1 1i; 1i 2] is symmetric but not Hermitian. A skew-symmetric matrix must have a zero diagonal. The default comparison is exact; use a tolerance for matrices computed with rounding.

Input arguments

A: Square numeric matrix.
tol: Non-negative tolerance, default 0.

Output arguments

tf: Logical scalar.

Example

Symmetric, skew and tolerance

issymmetric([1 2; 2 3])
issymmetric([0 1; -1 0])
issymmetric([0 1; -1 0], 'skew')
issymmetric([1 2; 2.0001 3], 0.001)

Output

ans = logical
   1
ans = logical
   0
ans = logical
   1
ans = logical
   0

issymmetric