Math calculators
Linear Algebra Calculators
16 tools
Small real matrices: Ax=b, det, inverse, rank, LU, QR, SVD, least squares, RREF, condition number, four fundamental subspaces, and eigenvalues. Same engine as the matrix workspace. Tools may appear in more than one topic.
Popular in Linear Algebra
Featured tools from the Family registry.
- Linear System Calculator Solve small linear systems Ax = b, plus det, inverse, rank, LU, Cholesky, QR, SVD, least squares, RREF, condition number, nullspace, column space, rowspace, left-nullspace, and eigenvalues. Same engine as the matrix workspace. Not a CAS. Runs locally.
- Matrix Determinant Calculator Determinant of a small real matrix. Same engine as Linear System and the matrix workspace. Not a CAS. Runs locally.
- Matrix Inverse Calculator Inverse of a small real matrix via Gauss–Jordan. Same engine as Linear System. Singular matrices fail. Not a CAS. Runs locally.
- Matrix Eigenvalues Calculator Eigenvalues and eigenvectors of a small real matrix via the characteristic polynomial. Same engine as Linear System. Not a CAS. Runs locally.
All Linear Algebra
Every live calculator in this family. URLs stay /calc/math/…
- Cholesky Factorization Calculator Lower Cholesky factorization of a small real symmetric positive-definite matrix. Same engine as Linear System. Not LU. Not a CAS. Runs locally.
- Column Space Calculator Column space (image) of a small real square matrix from RREF pivot columns. Same engine as Linear System. Trivial image is {0}. Left-nullspace is a sibling. Runs locally.
- Condition Number Calculator κ₁(A) = ‖A‖₁ ‖A⁻¹‖₁ for a small real square matrix. Same engine as Linear System. Singular matrices return infinite. Not a 2-norm product. Runs locally.
- Least Squares Calculator Linear least squares for a small real matrix, square or rectangular. Full column rank uses QR; otherwise SVD. Same engine as Linear System. Not Statistics regression. Runs locally.
- Left Nullspace Calculator Left-nullspace (cokernel) of a small real square matrix as ker(Aᵀ). Same engine as Linear System. Trivial left kernel is {0}. Not Jordan form. Runs locally.
- Linear System Calculator Solve small linear systems Ax = b, plus det, inverse, rank, LU, Cholesky, QR, SVD, least squares, RREF, condition number, nullspace, column space, rowspace, left-nullspace, and eigenvalues. Same engine as the matrix workspace. Not a CAS. Runs locally.
- LU Factorization Calculator Doolittle LU factorization with partial pivoting for a small real matrix. Same engine as Linear System. Not a CAS. Runs locally.
- Matrix Determinant Calculator Determinant of a small real matrix. Same engine as Linear System and the matrix workspace. Not a CAS. Runs locally.
- Matrix Eigenvalues Calculator Eigenvalues and eigenvectors of a small real matrix via the characteristic polynomial. Same engine as Linear System. Not a CAS. Runs locally.
- Matrix Inverse Calculator Inverse of a small real matrix via Gauss–Jordan. Same engine as Linear System. Singular matrices fail. Not a CAS. Runs locally.
- Matrix Rank Calculator Rank of a small real matrix via Gaussian elimination. Same engine as Linear System. Not a CAS. Runs locally.
- Nullspace Calculator Right nullspace of a small real square matrix from RREF. Same engine as Linear System. Trivial kernel is {0}. Left-nullspace is a sibling. Runs locally.
- QR Factorization Calculator Householder QR factorization of a small real matrix. Same engine as Linear System. Not a CAS. Runs locally.
- Row Space Calculator Row space of a small real square matrix from nonzero RREF rows. Same engine as Linear System. Trivial rowspace is {0}. Left-nullspace is a sibling. Runs locally.
- RREF Calculator Gauss–Jordan reduced row echelon form for a small real square matrix. Same engine as Linear System. Not a CAS. Runs locally.
- SVD Calculator Singular value decomposition of a small real square matrix. Same engine as Linear System. Least squares is a sibling discovery URL. Not a CAS. Runs locally.