Kronecker product

Last updated Jun 23, 2022

• Type atom
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• On linear algebra

Kronecker product is obtained by multiplying each term of the first Matrix/ Vector by the entire second matrix/vector. ¹ For example, with two qubits: $$
\ket{01} = \ket 0 \ket 1 = \ket 0 \otimes \ket 1
= \begin{pmatrix}1 \\ 0 \end{pmatrix} \otimes \begin{pmatrix}0 \\ 1 \end{pmatrix}
= \begin{pmatrix}1\begin{pmatrix}0 \\ 1 \end{pmatrix} \\ 0 \begin{pmatrix}0 \\ 1 \end{pmatrix}\end{pmatrix}
= \begin{pmatrix}0 \\ 1 \\ 0 \\ 0\end{pmatrix}.$$