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xerus
xerus
Commits
79b278c7
Commit
79b278c7
authored
May 17, 2017
by
Ben Huber
Browse files
small fixes and disclamer in nomenclature doc
parent
233a71c7
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#722
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in 7 minutes and 59 seconds
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doc/new/_posts/2000-12-15-nomenclature.md
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79b278c7
...
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@@ -14,7 +14,9 @@ names for the same concepts and at times even several concepts for the same name
we want to explain most terms as they are used throughout this library.
It is not strictly speaking necessary to read this chapter to successfully use the library, but it might very well help you find
the functions you were looking for if you are used to slightly different notation.
the functions you were looking for if you are used to slightly different notation. In particular this chapter is not meant to be
a complete introduction into the topic but is rather adressed at those that are already familiar with tensor arithmetic and
tensor networks.
## Tensors
...
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@@ -59,7 +61,7 @@ For every permutation $p:[d]\rightarrow[d]$ there is a **reshuffling** (or **reo
$$
\b
egin{align}
R:
\m
athbb{R}^{n_1
\t
imes n_2
\t
imes
\c
dots
\t
imes n_d} &
\r
ightarrow
\m
athbb{R}^{n_{p(1)}
\t
imes n_{p(2)}
\t
imes
\c
dots
\t
imes n_{p(d)}}
\\
T&
\m
apsto S
\;
:
\;
S[i_1, i_2,
\d
ots, i_d] = T[i_{p(1)}, i_{p(2)},
\d
ots, i_{p(d)}]
T&
\m
apsto S
\;
:
\;
S[i_1, i_2,
\d
ots, i_d] = T[i_{p
^{-1}
(1)}, i_{p
^{-1}
(2)},
\d
ots, i_{p
^{-1}
(d)}]
\e
nd{align}
$$
...
...
@@ -67,7 +69,7 @@ e.g. for matrices the transposition is a reordering or for tensors of degree $3$
$$
\b
egin{align}
\m
athbb{R}^{n_1
\t
imes n_2
\t
imes n_3} &
\r
ightarrow
\m
athbb{R}^{n_1
\t
imes n_3
\t
imes n2}
\\
\m
athbb{R}^{n_1
\t
imes n_2
\t
imes n_3} &
\r
ightarrow
\m
athbb{R}^{n_1
\t
imes n_3
\t
imes n
_
2}
\\
T&
\m
apsto S
\;
:
\;
S[i,j,k] = T[i,k,j]
\e
nd{align}
$$
...
...
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