Free · Physical and mathematical models
Small Matrix Kronecker Products
Calculate the Kronecker product of two matrices with one or two rows and columns, retaining each available output layout.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
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Formula and method
Calculate the Kronecker product of two matrices with one or two rows and columns, retaining each available output layout.
A⊗B replaces each entry a_ij by its scaled block a_ij B
Worked example
Enter these known values and leave the other values blank.
- Number of rows
- 2
- Number of columns
- 2
- Number of rows
- 2
- Number of columns
- 2
- a==1==
- 1
- a==2==
- 2
- b==1==
- 3
- b==2==
- 4
- x==1==
- 5
- x==2==
- 6
- y==1==
- 7
- y==2==
- 8
- p==1==
- 5
- p==2==
- 6
- p==3==
- 10
- p==4==
- 12
- q==1==
- 7
- q==2==
- 8
- q==3==
- 14
- q==4==
- 16
- r==1==
- 15
- r==2==
- 18
- r==3==
- 20
- r==4==
- 24
- s==1==
- 21
- s==2==
- 24
- s==3==
- 28
- s==4==
- 32
Assumptions and limitations
- This is a Kronecker or tensor product, not ordinary matrix multiplication. If A is m×n and B is p×q, the output is mp×nq.
- Both input dimensions are limited to one or two. Signed decimal entries and zero are valid.
- Captured inverse entry branches divide by the known multiplier; zero multipliers cannot uniquely recover an entry.
Common questions
How should I use an inverse?
Leave the required unknown empty and supply compatible known values. Multiple mathematical solutions or zero denominators can prevent a unique inverse.
What does this model assume?
This is a Kronecker or tensor product, not ordinary matrix multiplication. If A is m×n and B is p×q, the output is mp×nq.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.
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