Description Usage Arguments Value Examples

`H.coeff`

expands a *(d,d)*-dimensional Hermitian matrix `H`

with respect to
an orthonormal (in terms of the Frobenius inner product) basis of the space of Hermitian matrices.
That is, `H.coeff`

transforms `H`

into a numeric vector of *d^2* real-valued basis coefficients,
which is possible as the space of Hermitian matrices is a real vector space. Let *E_{nm}* be a
*(d,d)*-dimensional zero matrix with a 1 at location *(1, 1) ≤q (n,m) ≤q (d,d)*.
The orthonormal basis contains the following matrix elements; let *1 ≤ n ≤ d* and
*1 ≤ m ≤ d*,

- If
`n == m`

the real matrix element

*E_{nn}*- If
`n < m`

the complex matrix element

*2i/√ 2 E_{nm}*- If
`n > m`

the real matrix element

*2/√ 2 E_{nm}*

The orthonormal basis coefficients are ordered by scanning through the matrix `H`

in a row-by-row
fashion.

1 |

`H` |
if |

`inverse` |
a logical value that determines whether the forward basis transform ( |

If `inverse = FALSE`

takes as input a *(d,d)*-dimensional Hermitian matrix and outputs a numeric
vector of length *d^2* containing the real-valued basis coefficients. If `inverse = TRUE`

takes as input a
*d^2*-dimensional numeric vector of basis coefficients and outputs the corresponding *(d,d)*-dimensional
Hermitian matrix.

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