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matrix-calculator

A matrix calculator performs linear-algebra operations: addition, subtraction, scalar multiplication, matrix multiplication, transpose, determinant, inverse, rank, eigenvalues (for symbolic-friendly small matrices). Useful for linear-algebra coursework, computer graphics transform debugging, statistics (covariance matrices), and quick verification of hand calculations. The ZTools Matrix Calculator handles up to 10×10 with arbitrary numeric entries (integers, decimals, fractions if pre-converted), runs in the browser using a numerically-stable LU decomposition for inverse / determinant, and presents results with step-by-step intermediate values when relevant.

Use cases​

Verify a hand-computed inverse​

Linear-algebra homework. Calculator confirms (or shows where the error crept in).

Multiply transformation matrices for graphics​

A 3D engine pipeline: model × view × projection. Calculator multiplies these to verify the combined matrix.

Solve a linear system​

Ax = b → x = A⁻¹ b. Calculator finds the inverse and multiplies; useful for small systems.

Compute statistics covariance matrix​

For PCA, you need eigenvalues / eigenvectors of the covariance matrix. Calculator handles up to 10×10 — enough for most teaching scenarios.

How it works​

  1. Pick dimensions — 1×1 to 10×10 per matrix. Two-matrix ops (A + B) require matching shapes; multiplication requires inner dimensions to match.
  2. Enter values — Spreadsheet-style cells. Tab between cells for fast entry. Decimals, negatives, integers all supported.
  3. Pick operation — A+B, A−B, kA, A·B, A^T, det(A), A⁻¹, rank(A). Some ops need only one matrix.
  4. Read result — Result matrix displayed with the same precision. For inverse, also shown is det(A) — if it's 0, the matrix is singular and no inverse exists.

Examples​

Input: A = [[1,2],[3,4]], det(A)

Output: det = (1)(4) − (2)(3) = 4 − 6 = −2.

Input: Same A, inverse

Output: A⁻¹ = (1/det) × [[4,−2],[−3,1]] = [[−2, 1], [1.5, −0.5]].

Input: A·B for A 2×3, B 3×2

Output: Result is 2×2. Calculator handles matrix multiplication with conformable shapes.

Input: A is singular (det = 0)

Output: Inverse undefined. Calculator returns "no inverse — matrix is singular" rather than NaN.

Frequently asked questions​

Why does my answer differ slightly from textbook?

Floating-point arithmetic — small rounding errors. For exact arithmetic with fractions or symbolic results, use Wolfram Alpha or SymPy.

How big can the matrix be?

Up to 10×10 in this UI. For larger matrices, use NumPy / Octave / MATLAB — browser UI gets unwieldy.

Eigenvalues for non-symmetric matrices?

Limited support up to 4×4 — beyond that, characteristic polynomials get unstable to root-find numerically. Use a CAS for general cases.

Does it support complex numbers?

Real numbers only. Eigenvalues that turn out complex are reported as "complex pair" without computing the values.

Privacy?

All computation in browser.

Tips​

  • For small matrices (2×2 / 3×3), do the calculation by hand once to understand the formula — calculator confirms but doesn't teach.
  • When det = 0, no inverse exists. Check your matrix entries; one row or column is a linear combination of others.
  • For graphics transform debugging, multiply matrices in the right order — matrix multiplication is non-commutative (A·B ≠ B·A).
  • For larger problems, use NumPy: np.linalg.inv(A), np.linalg.det(A), np.linalg.matmul(A, B).

Try it now​

The full matrix-calculator runs in your browser at https://ztools.zaions.com/matrix-calculator — no signup, no upload, no data leaves your device.

Open the tool ↗

Last updated: 2026-05-06 · Author: Ahsan Mahmood · Edit this page on GitHub