Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
HyperTr
Compute the hypertrace of a given hypermatrix
Contributed by:
Riccardo Gatti
ResourceFunction["HyperTr"][h] gives the hypertrace of the cubical hypermatrix h. |
Details
A hypermatrix generalizes an ordinary matrix to an arbitrary-dimensional rectangular array. A cubical hypermatrix is the corresponding generalization of a square matrix.
The trace of a matrix is defined as the sum of the elements on the main diagonal. The main diagonal of the hypermatrix H is the set of values 
such that 
where 1≤i≤n. Their sum is the hypertrace, thus generalizing the ordinary matrix trace to tensors of arbitrary rank.
such that where 1≤i≤n. Their sum is the hypertrace, thus generalizing the ordinary matrix trace to tensors of arbitrary rank.Examples
Basic Examples
Calculate the hypertrace of a cubical hypermatrix with d=4 and n=2:
| In[1]:= | ![ResourceFunction["HyperTr"][
Array[Subscript[W, #1, #2, #3, #4] &, {2, 2, 2, 2}]]](https://www.wolframcloud.com/obj/resourcesystem/images/966/9667507e-df3d-479a-a600-3358a8f98429/7f8caa13a75bb197.png){kind=small} |
| Out[1]= |  |
Scope
Numeric values:
| In[2]:= | ![ResourceFunction["HyperTr"][{\!\(\*
TagBox[
RowBox[{"(", "", GridBox[{
{
RowBox[{"(", "",
TagBox[GridBox[{
{"0"},
{"3"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.5599999999999999]},
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}],
Column], "", ")"}],
RowBox[{"(", "",
TagBox[GridBox[{
{"1"},
{"4"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.5599999999999999]},
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}],
Column], "", ")"}]},
{
RowBox[{"(", "",
TagBox[GridBox[{
{"7"},
{"6"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.5599999999999999]},
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}],
Column], "", ")"}],
RowBox[{"(", "",
TagBox[GridBox[{
{"1"},
{"7"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.5599999999999999]},
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}],
Column], "", ")"}]}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}], "", ")"}],
Function[BoxForm`e$,
MatrixForm[BoxForm`e$]]]\), \!\(\*
TagBox[
RowBox[{"(", "", GridBox[{
{
RowBox[{"(", "",
TagBox[GridBox[{
{"4"},
{"7"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.5599999999999999]},
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}],
Column], "", ")"}],
RowBox[{"(", "",
TagBox[GridBox[{
{"0"},
{"5"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.5599999999999999]},
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}],
Column], "", ")"}]},
{
RowBox[{"(", "",
TagBox[GridBox[{
{"9"},
{"7"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.5599999999999999]},
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}],
Column], "", ")"}],
RowBox[{"(", "",
TagBox[GridBox[{
{"8"},
{"7"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.5599999999999999]},
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}],
Column], "", ")"}]}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}], "", ")"}],
Function[BoxForm`e$,
MatrixForm[BoxForm`e$]]]\)}]](https://www.wolframcloud.com/obj/resourcesystem/images/966/9667507e-df3d-479a-a600-3358a8f98429/3870347406e65861.png) |
| Out[2]= |  |
Publisher
Related Links
Version History
- 1.0.0 – 21 November 2022
Source Metadata
Related Resources
Related Symbols
License Information
This work is licensed under a Creative Commons Attribution 4.0 International License