Matrix modulo calculator form
Use integers only. Select an operation, set dimensions, enter matrices, then calculate.
Formula used
Single entry modulo: r = a mod n
Normalized entry: r = ((a % n) + n) % n
Addition under modulo: (A + B) mod n
Subtraction under modulo: (A - B) mod n
Multiplication under modulo: Cij = (Σ AikBkj) mod n
Power under modulo: Ak mod n, computed by repeated squaring
Determinant under modulo: det(A) mod n
Negative values are wrapped into the range 0 to n−1, so results stay consistent for modular arithmetic.
How to use this calculator
- Select the size of Matrix A.
- Pick a modulus greater than zero.
- Choose the operation you want to apply.
- Enter integer values for Matrix A.
- Enter Matrix B if the chosen operation needs it.
- Add an exponent when using the power option.
- Click the calculate button.
- Review the result, summary cards, downloads, and heatmap.
Example data table
| Example | Matrix A | Matrix B | Modulus | Result |
|---|---|---|---|---|
| Element-wise modulo | [[8, -3], [14, 5]] | Not needed | 7 | [[1, 4], [0, 5]] |
| Addition modulo | [[8, -3], [14, 5]] | [[2, 7], [-4, 6]] | 7 | [[3, 4], [3, 4]] |
| Multiplication modulo | [[1, 2], [3, 4]] | [[5, 6], [7, 8]] | 9 | [[1, 4], [7, 4]] |
FAQs
1. What does matrix modulo mean?
Matrix modulo reduces every entry by a positive modulus and keeps the remainder in a fixed range. It is common in number theory, coding, cryptography, and discrete mathematics.
2. Why do negative matrix entries become positive?
The calculator normalizes negative remainders with ((a % n) + n) % n. That places every final value between 0 and n−1, which is the standard modular range.
3. When should I use matrix addition modulo?
Use addition modulo when combining two same-sized matrices in modular arithmetic. This is useful for classroom exercises, transformation tables, and finite-system computations.
4. Does matrix multiplication modulo need matching dimensions?
Yes. The number of columns in Matrix A must equal the number of rows in Matrix B. The calculator handles this layout automatically for the multiplication option.
5. Why must powers and determinants use square matrices?
A determinant exists only for square matrices. Matrix powers also require a square matrix because repeated multiplication must preserve the same dimensions after every step.
6. Can this tool help with modular arithmetic homework?
Yes. It is useful for checking element-wise reductions, matrix sums, products, powers, and determinants. The example table and heatmap also make result patterns easier to study.
7. What do the CSV and PDF downloads include?
They export the displayed result matrix. CSV works well for spreadsheets, while PDF is useful for reports, assignments, or sharing a formatted snapshot of the output.
8. What does the Plotly heatmap show?
The heatmap visualizes the final matrix values. It helps you compare rows, spot repeated structures, and see where entries cluster after modular reduction.