Linear Algebra Calculators

19 free linear algebra calculators in Math.

Cholesky Decomposition CalculatorFactor a symmetric positive-definite matrix into L·Lᵀ with definiteness verification.
Cross Product CalculatorFind the cross product of two 3D vectors with magnitude and direction.
Dot Product CalculatorCompute the dot (inner) product of two vectors with geometric interpretation.
Gaussian Elimination CalculatorRow-reduce any matrix to echelon and reduced row-echelon form with pivot tracking.
Linear Transformation CalculatorApply a matrix transformation to a vector and visualise the mapped coordinates.
LU Decomposition CalculatorFactor a square matrix into lower and upper triangular matrices with partial pivoting.
Matrix Addition CalculatorAdd two matrices element-wise with dimension validation and step-by-step output.
Matrix Determinant CalculatorCompute the determinant of any square matrix using LU factorisation with partial pivoting.
Matrix Eigenvalues CalculatorFind eigenvalues via the characteristic polynomial (2×2, 3×3) or QR iteration (larger symmetric).
Matrix Eigenvectors CalculatorCompute eigenvectors for each eigenvalue of a 2×2 or 3×3 real matrix.
Matrix Inverse CalculatorCompute the inverse of a square matrix via LU decomposition with singularity detection.
Matrix Multiplication CalculatorMultiply two matrices of compatible dimensions with full row-by-column working.
Matrix Rank CalculatorDetermine the rank of a matrix by row-reducing to echelon form.
Norm CalculatorCompute L1, L2 (Euclidean), and L-infinity norms of a vector.
Projection Matrix CalculatorBuild the orthogonal projection matrix onto the column space of a given matrix.
QR Decomposition CalculatorDecompose a matrix into an orthogonal Q and upper-triangular R via Gram-Schmidt.
Vector Addition CalculatorAdd two or more vectors component-wise in any dimension and show the resultant.
Vector Angle CalculatorCalculate the angle between two vectors using the dot product formula.
Vector Projection CalculatorProject one vector onto another and compute the scalar and vector projections.