writer
6,694
edits
Changes
Jump to navigation
Jump to search
Line 10:
Line 10: + Line 45:
Line 46: + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Manuals/calci/MATRIXTENSORPRODUCT (view source)
Revision as of 20:18, 12 July 2017
, 20:18, 12 July 2017no edit summary
*The Tensor product is defined by the product two vector spaces V and W is itself a Vector space.
*The Tensor product is defined by the product two vector spaces V and W is itself a Vector space.
*It is denoted by <math>V\otimes W</math>.
*It is denoted by <math>V\otimes W</math>.
*A [http://wiki.zcubes.com/Manuals/calci/DYADIC DYADIC] product is the special case of the tensor product between two vectors of the same dimension.
*The tensor product of V and W is the vector space generated by the symbols <math>v\otimes w </math>, with <math>v \isin V</math> and <math>w \isin W</math>.
*The tensor product of V and W is the vector space generated by the symbols <math>v\otimes w </math>, with <math>v \isin V</math> and <math>w \isin W</math>.
*The tensor product from the direct sum vector space, whose dimension is the sum of the dimensions of the two summands:
*The tensor product from the direct sum vector space, whose dimension is the sum of the dimensions of the two summands:
a_{21}b_{21} & a_{21}b_{22} & a_{22}b_{21} & a_{22}b_{22}
a_{21}b_{21} & a_{21}b_{22} & a_{22}b_{21} & a_{22}b_{22}
\end{bmatrix} </math>
\end{bmatrix} </math>
==Examples==
1. MATRIXTENSORPRODUCT([[2,6],[-4,9]],[[8,5],[3,12]])
{| class="wikitable"
|-
|16 ||10 ||48 ||30
|-
|6 ||24 ||18|| 72
|-
| -32|| -20 || 72||45
|-
| -12 || -48 || 27 ||108
|}
2. MATRIXTENSORPRODUCT([[3,7.3,6],[10,11,-6],[8,5,3]],[[12,4,-5],[6,10,3],[3.5,9,5.4]])
{| class="wikitable"
|-
|36 || 12|| -15 ||87.6 ||29.2||-36.5||72||24||-30
|-
|18 || 30 ||9 ||43.8|| 73||21.9||36|| 60|| 18
|-
|10.5 ||27||16.200000000000003||25.55|| 65.7||39.42||21||54||32.400000000000006
|-
|120 || 40||-50||132||44||-55|| -72||-24||30
|-
|60 || 100||30 ||66 || 110 || 33 || -36 ||-60 ||-18
|-
|35 || 90 || 54 ||38.5||99 ||59.400000000000006 || -21||-54||-32.400000000000006
|-
|96 || 32 || -40 || 60 || 20 || -25 || 36 || 12 ||-15
|-
|48 || 80 ||24 || 30 || 50 || 15 || 18 || 30 ||9
|-
|28 || 72 || 43.2 || 17.5 || 45 ||27 ||10.5 || 27||16.200000000000003
|}
==See Also==
*[[Manuals/calci/CHOLESKYFACTORIZATION| CHOLESKYFACTORIZATION]]
*[[Manuals/calci/CONFERENCE| CONFERENCE]]
*[[Manuals/calci/PASCAL| PASCAL]]
==References==
*[https://en.wikipedia.org/wiki/Tensor_product Tensor Product]
*[[Z_API_Functions | List of Main Z Functions]]
*[[ Z3 | Z3 home ]]