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 $V\otimes W$.
• 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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle dim (V \otimes W)= dim V +dim W }

• Now consider any 2x2 matrices:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{bmatrix} a_{11}b_{11} a_{11}b_{12} a_{12}b_{11} a_{12}b_{12}\\ \end{bmatrix} }