Matrix Tool
Enter matrices up to six rows and columns to perform arithmetic, determinant, inverse, rank, row reduction, eigenvalue and linear-system calculations. Explore the resulting matrix through an interactive heatmap and bar chart, then export results in several formats.
Table of Contents
Highlights
- 13 matrix operations, including inverses and eigenvalues
- Editable matrices up to 6 × 6
- Interactive result heatmap and value chart
- Adjustable display precision and quick matrix inputs
- Export results as CSV, JSON, TXT or PNG
How Matrix Tool Works?
A matrix is a rectangular array of numbers. This tool accepts matrices with 1 to 6 rows and 1 to 6 columns and computes operations selected by the user. Addition and subtraction work entry by entry and require matching dimensions. Matrix multiplication combines rows of A with columns of B, requiring the column count of A to match the row count of B.
For square matrices, the determinant indicates whether an inverse exists. The inverse and the solution of Ax = b use elimination with pivot selection. Reduced row echelon form and rank use row operations, while trace adds the main diagonal. Transposition swaps rows with columns. Scalar multiplication multiplies each entry by k; integer powers multiply A repeatedly (with A⁰ equal to the identity). For a 2 × 2 matrix, the eigenvalues are the roots of its characteristic polynomial.
| Operation | Input requirement | Result |
|---|---|---|
| A ± B | Same dimensions | Entrywise sum or difference |
| A × B | Columns of A = rows of B | Matrix product |
| Determinant, inverse, trace, powers | Square A | Scalar or matrix |
| Ax = b | Square, invertible A; one-column b | Solution vector |
| Eigenvalues | 2 × 2 A | Two real or complex values |
| Transpose, rank, row reduction | Any supported A | Matrix or rank |
The display reports a formatted result and, where relevant, a determinant, rank or solution summary. A colour-coded heatmap and value-distribution chart reveal the sizes and signs of numeric result entries.
Practical Use Cases
Students: Check matrix products, determinants, inverses and row-reduced forms while studying linear algebra, and compare numerical results against hand calculations.
Engineers: Apply small transformation matrices, multiply compatible arrays and solve compact systems of simultaneous linear equations.
Data analysts: Explore transposes, matrix rank and entry distributions when reviewing small tables of numeric coefficients.
Computer graphics learners: Experiment with matrix multiplication, powers and inverses to understand composed or reversed linear transformations.
Teachers: Demonstrate how changing matrix entries affects the determinant, eigenvalues and visual patterns in the output.
Accuracy and Limitations
Calculations use JavaScript floating-point arithmetic, so results are approximate and may show rounding errors, especially for ill-conditioned matrices. Inputs are limited to 6 × 6, displayed precision can be set to 2, 4, 6, 8 or 10 decimal places, and elimination treats pivots smaller than 10−10 as zero. Eigenvalues are supported only for 2 × 2 matrices; matrix exponents must be integers between −20 and 20. Solving Ax = b requires a square, invertible A, and the tool rejects numeric result entries with absolute values exceeding 1014. Complex eigenvalues are displayed as text and are not included in numeric charts.
