Manuals/calci/MATRIXTENSORPRODUCT

MATRIXTENSORPRODUCT (a,b)

• $a$ and $b$ are any two matrices.

Description

• This function shows the Tensor product of the matrix.
• In $MATRIXTENSORPRODUCT(a,b)$ , $a$ and $b$ are any two matrices.
• Here matrices $a$ and $b$ should be square matrix with same order.
• Tensor product is denoted by $\otimes$.
• 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 $V\otimes W$.
• A 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 $v\otimes w$, with $v\in V$ and $w\in W$.
• The tensor product from the direct sum vector space, whose dimension is the sum of the dimensions of the two summands:

$dim(V\otimes W)=dimV+dimW$

• Now consider any 2x2 matrices:

${\begin{bmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{bmatrix}}\otimes {\begin{bmatrix}b_{11}&b_{12}\\b_{21}&b_{22}\end{bmatrix}}={\begin{bmatrix}a_{11}{\begin{bmatrix}b_{11}&b_{12}\\b_{21}&b_{22}\end{bmatrix}}a_{12}{\begin{bmatrix}b_{11}&b_{12}\\b_{21}&b_{22}\end{bmatrix}}\\a_{21}{\begin{bmatrix}b_{11}&b_{12}\\b_{21}&b_{22}\end{bmatrix}}a_{22}{\begin{bmatrix}b_{11}&b_{12}\\b_{21}&b_{22}\end{bmatrix}}\end{bmatrix}}$ = ${\begin{bmatrix}a_{11}b_{11}&a_{11}b_{12}&a_{12}b_{11}&a_{12}b_{12}\\a_{11}b_{21}&a_{11}b_{22}&a_{12}b_{21}&a_{12}b_{22}\\a_{21}b_{11}&a_{21}b_{12}&a_{22}b_{11}&a_{22}b_{12}\\a_{21}b_{21}&a_{21}b_{22}&a_{22}b_{21}&a_{22}b_{22}\end{bmatrix}}$

Examples

1. MATRIXTENSORPRODUCT([[2,6],[-4,9]],[[8,5],[3,12]])

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]])

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

• CHOLESKYFACTORIZATION
• CONFERENCE
• PASCAL

References

• Tensor Product

• List of Main Z Functions

• Z3 home