Enter the four entries of each matrix by row and column. All inputs are dimensionless real numbers; negative numbers, zero and decimals are allowed. The calculator returns C = A ⊗ B as sixteen individually labelled entries, ordered across each row of the 4×4 result. The order of the inputs matters: A supplies the block multipliers, and B supplies the entries inside each block.
Place A11 × B in the upper-left block, A12 × B in the upper-right block, A21 × B in the lower-left block and A22 × B in the lower-right block. For example, C23 is A12 × B21. This construction follows the Kronecker product convention described in the Wolfram KroneckerProduct documentation.
Ordinary matrix multiplication of two 2×2 matrices produces a 2×2 matrix using sums of products. Here, the result is 4×4, and each entry requires a single multiplication.
The default inputs use A with rows (1, 2) and (3, 4), and B with rows (5, 6) and (7, 8). The four blocks are B, 2B, 3B and 4B. The table below shows the expected result for these default inputs; it is a fixed example.
| Result row | Column 1 | Column 2 | Column 3 | Column 4 |
|---|---|---|---|---|
| 1 | 5 | 6 | 10 | 12 |
| 2 | 7 | 8 | 14 | 16 |
| 3 | 15 | 18 | 20 | 24 |
| 4 | 21 | 24 | 28 | 32 |
Does swapping A and B give the same result?
Generally, no. Swapping the matrices changes which entries multiply the blocks and can change their positions. Enter the matrices in the order required by A ⊗ B.
Can either matrix be singular or contain zeros?
Yes. No inverse or division is required. A zero entry in A produces a zero 2×2 block in the corresponding position.
Can I use complex entries or larger matrices?
This calculator accepts two real 2×2 matrices only. Each input is one numeric entry, and the result is reported as sixteen scalar values.
How can I check the ordering with an identity matrix?
Set A11 and A22 to 1, and A12 and A21 to 0. The result has B in its upper-left and lower-right blocks, with zero blocks elsewhere.