Linear Algebra Calculators
Linear algebra is the mathematics of vectors, matrices and linear maps. It underlies computer graphics, machine learning, engineering simulation, cryptography and most of applied mathematics, and it is a core subject in B.Sc Mathematics, B.Tech and BCA programmes.
The calculators below work with exact fractions, so a rank, a reduced row echelon form or an inverse is never spoiled by rounding error. Each tool shows the row operations or formula used, so you can follow the method and compare it with your own working.
A good order for beginners is: matrix operations and rank, then Gaussian elimination and linear systems, then determinants and inverses, and finally eigenvalues and eigenvectors.
Linear Algebra tools
Matrix Operations & Rank Calculator
Add, subtract, multiply, scale and transpose any-size matrices, then find rank, REF and RREF — every row operation explained, with PDF export.
Inverse Matrix Calculator
Find the inverse of a 2×2 up to 5×5 matrix by Gauss–Jordan elimination, with exact fractions and a verification.
Linear Equations Solver
Solve a system of linear equations by Gauss–Jordan elimination: unique, infinite or no solution, with every row operation.
Null Space & Column Space Calculator
Find a basis and the dimension of the column space, row space, null space and left null space of a matrix, with exact verification.
Gram-Schmidt Calculator
Orthogonalize and normalize vectors with the Gram–Schmidt process using exact fractions and radicals, with every projection shown.
Matrix Diagonalization Calculator
Diagonalize a 2×2 or 3×3 matrix as A = P D P⁻¹ with exact eigenvalues and vectors, and compute powers Aᵏ.
Eigenvalues & Eigenvectors Calculator
Characteristic polynomial, eigenvalues and eigenvectors of 2×2 and 3×3 matrices, exact where possible, with every step.
Matrix Determinant & Inverse
Exact determinant and inverse for 2×2 and 3×3 matrices, with cofactor / adjugate steps and a verification check.