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Kronecker Product

Tool to calculate a Kronecker matrix product in computer algebra. The Kronecker product is a special case of tensor multiplication on matrices.

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Kronecker Product -

Tag(s) : Mathematics,Algebra,Symbolic Computation

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Kronecker Product

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Kronecker Product



Tool to calculate a Kronecker matrix product in computer algebra. The Kronecker product is a special case of tensor multiplication on matrices.

Answers to Questions

How to multiply 2 matrices with Kronecker?

Consider \( M_1=[a_{ij}] \) a matrix of \( m \) lines and \( n \) columns and \( M_2=[b_{ij}] \) a matrix of \( p \) lines and \( q \) columns. The Kronecker product is noted with \( M_1 \otimes M_2 = [c_{ij}] \) is a larger matrix of \( m \times p \) lines and \( n \times q \) columns, with : $$ \forall i, j : c_{ij} = a_{ij}.B $$

$$ M=\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{pmatrix} \otimes \begin{pmatrix} 7 & 8 \\ 9 & 10 \end{pmatrix} = \begin{pmatrix} 7 & 8 & 14 & 16 & 21 & 24 \\ 9 & 10 & 18 & 20 & 27 & 30 \\ 28 & 32 & 35 & 40 & 42 & 48 \\ 36 & 40 & 45 & 50 & 54 & 60 \end{pmatrix} $$

What are matrix Kronecker multiplication properties?

Associativity : $$ A \otimes (B+ \lambda\ \cdot C) = (A \otimes B) + \lambda (A \otimes C) $$

$$ (A + \lambda\ \cdot B) \otimes C = (A \otimes C) + \lambda (B \otimes C) $$

$$ A \otimes ( B \otimes C) = (A \otimes B) \otimes C $$

$$ (A \otimes B) (C \otimes D) = (A C) \otimes (B D) $$

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