Matrices/Kronecker product/Definition
Kronecker product
The
Kronecker product
of matrices
A
=
(
a
i
j
)
1
≤
i
≤
m
,
1
≤
j
≤
n
{\displaystyle {}A={\left(a_{ij}\right)}_{1\leq i\leq m,\,1\leq j\leq n}\,}
and
B
=
(
b
k
ℓ
)
1
≤
k
≤
p
,
1
≤
ℓ
≤
r
{\displaystyle {}B={\left(b_{k\ell }\right)}_{1\leq k\leq p,\,1\leq \ell \leq r}\,}
is given by
(
a
i
j
⋅
b
k
ℓ
)
1
≤
i
≤
m
,
1
≤
k
≤
p
;
1
≤
j
≤
n
,
1
≤
ℓ
≤
r
.
{\displaystyle {\left(a_{ij}\cdot b_{k\ell }\right)}_{1\leq i\leq m,\,1\leq k\leq p;\,1\leq j\leq n,\,1\leq \ell \leq r}.}
