Free · Mathematics models
Transpose a Matrix up to Four by Four
Swap rows and columns for all captured matrix dimensions from one through four.
- Formula & worked example
- Private in your browser
- No signup
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
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
The input rows (1,2) and (3,4) transpose to rows (1,3) and (2,4).
The transposed entry in row j and column i equals the original entry in row i and column j.
Worked example
Enter these known values and leave the other values blank.
- a==1==
- 1
- a==2==
- 2
- b==1==
- 3
- b==2==
- 4
- t==11==
- 1
- t==12==
- 3
- t==21==
- 2
- t==22==
- 4
Assumptions and limitations
- Entries are ordinary real numbers; dimension selectors retain all sixteen supported rectangular shapes.
- The transformation is one way: edit original entries, then inspect the transposed outputs. Hidden entries remain stored when dimensions change.
- This model does not compute inverses, determinants or complex conjugates.
- Clear the unknown numerical field before using a supported inverse; selection controls retain their captured branches.
Common questions
What assumptions matter for this model?
Entries are ordinary real numbers; dimension selectors retain all sixteen supported rectangular shapes.
What does this model leave out?
This model does not compute inverses, determinants or complex conjugates.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.