# OpenMath Content Dictionary: linalg6

Canonical URL:
http://www.openmath.org/cd/linalg6.ocd
CD Base:
http://www.openmath.org/cd
CD File:
linalg6.ocd
CD as XML Encoded OpenMath:
linalg6.omcd
Defines:
matrix_tensor, vector_tensor
Date:
1999-07-15
Version:
2
Review Date:
2003-04-01
Status:
experimental

This CD contains symbols for the construction of some new vectors and matrices from old ones by means of the tensor product.

## matrix_tensor

Description:

This symbol denotes a n-nary function which is used to construct the tensor product matrix of its arguments, which must be matrices.

Commented Mathematical property (CMP):
If A is an m x r matrix B is an n x s matrix, then their Kronecker product is the m n x rs matrix whose i + (k-1) m, j + (l-1) n entry is A_{i,j} B_{k,l},
Formal Mathematical property (FMP):
$\mathrm{rowcount}\left(A\right)=m\wedge \mathrm{columncount}\left(A\right)=n⇒{\mathrm{matrix_tensor}\left(A,B\right)}_{\left(i+\left(k-1\right)m,j+\left(l-1\right)n\right)}={A}_{\left(i,j\right)}{B}_{\left(k,l\right)}$
Signatures:
sts

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## vector_tensor

Description:

This symbol denotes a n-nary function which is used to construct the tensor product vector of its arguments, which must be vectors.

Signatures:
sts

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