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Home › linear algebra › Linear Algebra Calculators

Linear Algebra Calculators

Step-by-step calculators for matrices, vectors, and linear systems — every operation shows its full working.

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3Calculators
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Step-by-step Solutions

Why Use These Tools?

Linear algebra is built on procedures — row reduction, matrix inversion, dot products, eigenspaces — and the only way to truly understand them is to see every step, not just the final number. Each calculator here shows the complete working process alongside the result.

The Matrix Calculator covers over 20 operations across four categories: single-matrix (determinant, inverse, transpose, rank, trace, LU decomposition), two-matrix arithmetic (multiplication, Kronecker product, commutator, anti-commutator), scalar operations, and linear system solving. A live explanation panel updates as you select each operation, and a calculation history tracks every result in the session.

The Vector Calculator handles everything from basic magnitude and normalization to cross products, projections, Gram-Schmidt orthogonalization, linear independence checks, and span verification — supporting vectors of any dimension from 2D to 10D.

The Linear Systems Calculator solves up to 10×10 systems using Gaussian Elimination, Gauss-Jordan, Cramer's Rule, or the Inverse Method. It renders the full augmented matrix, shows row operations step by step, and plots the solution graphically for two-variable systems.

All three tools are free, require no sign-up, and work on any device.