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.