Matrix Calculator

How it works

Every entry is stored as a BigInt numerator and a positive BigInt denominator, reduced by their greatest common divisor. For example, 0.1 becomes exactly 1/10, and 2/6 becomes 1/3. Arithmetic reduces fractions throughout the calculation. This avoids floating-point pivot tolerances and preserves exact zero tests, but it does not support symbolic expressions, variables, complex numbers, exponents or arbitrary-size matrices.

Addition and subtraction combine corresponding entries and require identical dimensions. Multiplication A × B requires the number of columns in A to equal the number of rows in B; every result entry is a row-by-column dot product. Transpose swaps rows and columns. Determinant and inverse require a square matrix. Determinants use exact Gaussian elimination, tracking row swaps and pivot products. Inversion applies Gauss–Jordan row operations to [A | I]; if the left side becomes I, the right side is A⁻¹. A missing nonzero pivot proves singularity for the supplied exact rational matrix, so the tool reports that an inverse does not exist. It never invents an inverse using an epsilon threshold.

Enter one matrix row per line. Commas, spaces and tabs separate entries; all rows must have the same number of entries. Thus 1,234 means two entries, 1 and 234, not a grouped thousands value. Empty comma fields, internal blank rows and ragged rows are rejected. Leading and trailing whitespace is ignored. Integers and decimals may have an ordinary + or - sign, up to 12 digits before and 12 digits after a decimal point. A fraction has a signed integer numerator and denominator, each up to 12 digits; zero denominators are rejected and a negative denominator is normalized. Scientific notation, percent signs, formulas, Unicode minus signs and evaluated expressions are not accepted.

Each matrix is bounded to 1–6 rows, 1–6 columns and 16 KiB of text. Every reduced intermediate numerator and denominator is bounded to 4,096 binary digits; a calculation exceeding that budget stops with a size message instead of attempting unbounded computation. The synchronous bounded operation has no background upload or hidden job. Changing inputs or operation, Clear, or Reset example removes previous results and downloads immediately. The initial 2 × 2 example and reset example are labelled and excluded from workflow measurement until the user edits the inputs.

CSV preserves the rectangular result with exact reduced entries. Spreadsheet software can interpret 1/2 as a date, so import every CSV column as Text. No spreadsheet formula is inserted to force a display format. JSON preserves exact strings, explicit numerator/denominator strings, normalized input matrices and the method steps, making it a safer format when exact fraction types matter. Determinants are exported as a 1 × 1 matrix. Downloaded files contain the retained calculation, so review them before sharing. No entry is stored in a URL or sent to analytics. Anonymous workflow measurement records fixed task and outcome labels, never matrix values.

Common use cases

• Multiply rectangular matrices and keep a checkable row-by-column result.
• Compute an inverse without rounding decimal inputs before elimination.
• Find an exact determinant, including row swaps and singular matrices.
• Export reduced fractions for teaching notes, calculations or another application.

Frequently asked questions

Standards and limitations

• OpenStax: matrices and matrix operations
• OpenStax: matrix inverses and augmented row operations