R: Test if a Matrix or other Object is Symmetric (Hermitian)

isSymmetric {base} | R Documentation

## Test if a Matrix or other Object is Symmetric (Hermitian)

### Description

Generic function to test if `object` is symmetric or not. Currently only a matrix method is implemented, where a `complex` matrix `Z` must be “Hermitian” for `isSymmetric(Z)` to be true.

### Usage

    isSymmetric(object, ...)
    ## S3 method for class 'matrix'
    isSymmetric(object, tol = 100 * .Machine$double.eps,
                tol1 = 8 * tol, ...)

### Arguments

`object` | any R object; a `matrix` for the matrix method.
`tol` | numeric scalar >= 0. Smaller differences are not considered, see `all.equal.numeric`.
`tol1` | numeric scalar >= 0. `isSymmetric.matrix()` ‘pre-tests’ the first and last few rows for fast detection of ‘obviously’ asymmetric cases with this tolerance. Setting it to length zero will skip the pre-tests.
`...` | further arguments passed to methods; the matrix method passes these to `all.equal`. If the row and column names of `object` are allowed to differ for the symmetry check do use `check.attributes = FALSE`!

### Details

The `matrix` method is used inside `eigen` by default to test symmetry of matrices up to rounding error, using `all.equal`. It might not be appropriate in all situations.

Note that a matrix `m` is only symmetric if its `rownames` and `colnames` are identical. Consider using `unname(m)`.

### Value

logical indicating if `object` is symmetric or not.

### See Also

`eigen` which calls `isSymmetric` when its `symmetric` argument is missing.

### Examples

    isSymmetric(D3 <- diag(3)) # -> TRUE

    D3[2, 1] <- 1e-100
    D3
    isSymmetric(D3) # TRUE
    isSymmetric(D3, tol = 0) # FALSE for zero-tolerance

    ## Complex Matrices - Hermitian or not
    Z <- sqrt(matrix(-1:2 + 0i, 2)); Z <- t(Conj(Z)) %*% Z
    Z
    isSymmetric(Z)      # TRUE
    isSymmetric(Z + 1)  # TRUE
    isSymmetric(Z + 1i) # FALSE -- a Hermitian matrix has a *real* diagonal

    colnames(D3) <- c("X", "Y", "Z")
    isSymmetric(D3)                         # FALSE (as row and column names differ)
    isSymmetric(D3, check.attributes=FALSE) # TRUE  (as names are not checked)

[Package base version 4.0.5 Index]