Tensor Product Calculator

What Is the Tensor Product of Matrices?

The tensor product of two matrices, also called the Kronecker product, produces a larger block matrix. Each entry of the first matrix is multiplied by the entire second matrix. If $A$ is $m \times n$ and $B$ is $p \times q$, then $A \otimes B$ is $(mp) \times (nq)$.

For standard matrix multiplication, see our Matrix Multiply Calculator and Hadamard Product Calculator.

Kronecker Product Formula

For $2 \times 2$ matrices:

$$A \otimes B = \begin{bmatrix} a_{11}B & a_{12}B \\ a_{21}B & a_{22}B \end{bmatrix}$$

The Kronecker product is not commutative: $A \otimes B \neq B \otimes A$ in general, but it is associative and bilinear.

Worked Example

If $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & 5 \\ 6 & 7 \end{bmatrix}$, then $A \otimes B$ is a $4 \times 4$ matrix with blocks $a_{ij} \cdot B$.