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,
n == m
the real matrix element E_{nn}
n < m
the complex matrix element 2i/√ 2 E_{nm}
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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