Manuals/calci/TENSORPRODUCT - Revision history

Devika: /* Examples */

2022-02-22T09:06:14Z

Examples

Devika: /* Examples */

2022-02-22T09:05:08Z

Examples

Devika: /* Examples */

2022-02-22T08:59:37Z

Examples

Devika: /* See Also */

2019-05-02T19:36:15Z

Devika: Created page with "
'''TENSORPRODUCT (a,b) '''

OR
'''MATRIXTENSORPRODUCT (a,b) '''

* $a$ and $b$ ..."

2017-07-12T23:15:56Z

Created page with "<div style="font-size:30px">'''TENSORPRODUCT (a,b) '''</div><br/> OR <div style="font-size:30px">'''MATRIXTENSORPRODUCT (a,b) '''</div><br/> *<math>a</math> and <math>b</math>..."

New page

<div style="font-size:30px">'''TENSORPRODUCT (a,b) '''</div><br/>
OR
<div style="font-size:30px">'''MATRIXTENSORPRODUCT (a,b) '''</div><br/>
*<math>a</math> and <math>b</math> are any two matrices.

==Description==
*This function shows the Tensor product of the matrix.
*In <math>TENSORPRODUCT (a,b)</math> , <math>a</math> and <math>b</math> are any two matrices.
*Here matrices <math>a</math> and <math>b</math> should be square matrix with same order.
*Tensor product is denoted by <math>\otimes</math>.
*Tensor product is different from general product.
*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>.
*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 from the direct sum vector space, whose dimension is the sum of the dimensions of the two summands:
<math>dim (V \otimes W)= dim V +dim W </math>
*Now consider any 2x2 matrices:
<math>\begin{bmatrix}
a_{11} & a_{12} \\
a_{21} & a_{22}
\end{bmatrix}\otimes \begin{bmatrix}
b_{11} & b_{12} \\
b_{21} & b_{22}
\end{bmatrix} =
\begin{bmatrix}
a_{11}\begin{bmatrix}
b_{11} & b_{12} \\
b_{21} & b_{22}
\end{bmatrix} a_{12} \begin{bmatrix}
b_{11} & b_{12} \\
b_{21} & b_{22}
\end{bmatrix} \\

a_{21} \begin{bmatrix}
b_{11} & b_{12} \\
b_{21} & b_{22}
\end{bmatrix}
a_{22} \begin{bmatrix}
b_{11} & b_{12} \\
b_{21} & b_{22}
\end{bmatrix}
\end{bmatrix} </math> =
<math>\begin{bmatrix}
a_{11}b_{11} & a_{11}b_{12} & a_{12}b_{11} & a_{12}b_{12}\\
a_{11}b_{21} & a_{11}b_{22} & a_{12}b_{21} & a_{12}b_{22}\\
a_{21}b_{11} & a_{21}b_{12} & a_{22}b_{11} & a_{22}b_{12}\\
a_{21}b_{21} & a_{21}b_{22} & a_{22}b_{21} & a_{22}b_{22}
\end{bmatrix} </math>

==Examples==
1. TENSORPRODUCT([[2,3],[1,0]],[[10,2],[6,-18]])
{| class="wikitable"
|-
|20 ||4 ||30 ||6
|-
|12 ||-36 ||18||-54
|-
| 10|| 2 ||0 || 0
|-
| 6 || -18 || 0 ||0
|}

2. TENSORPRODUCT([[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 ]]

@@ Line 84: / Line 84: @@
 |}
-. TENSORPRODUCT([[1,2,3]],[[4,5,6]]).print()
+.TENSORPRODUCT([[1,2,3]],[[4,5,6]]).print()
+[

@@ Line 89: / Line 89: @@
 	[4,5,6,8,10,12,12,15,18	]
+]
 . TENSORPRODUCT([[1],[2],[3]],[[4],[5],[6]]).print()
+[
 	[4	],
@@ Line 109: / Line 111: @@
 	[18	]
+]
 . TENSORPRODUCT([[1],[2],[3]],[[4],[5]]).print()
+[
 	[4	],

@@ Line 83: / Line 83: @@
 |28 ||	72 || 43.2 || 17.5 || 45 ||27 ||10.5 ||	27||16.200000000000003
 |}
 ==Related Videos==

Manuals/calci/TENSORPRODUCT - Revision history

Devika: /* Examples */

Devika: /* Examples */

Devika: /* Examples */

Devika: /* See Also */

Devika: Created page with "'''TENSORPRODUCT (a,b) ''' OR '''MATRIXTENSORPRODUCT (a,b) ''' *a and b..."

Devika: Created page with "
'''TENSORPRODUCT (a,b) '''

OR
'''MATRIXTENSORPRODUCT (a,b) '''

* $a$ and $b$ ..."