Linear Algebra

Determinant of a square matrix (up to 10x10) by LU with partial pivoting, flagging a numerically singular matrix.

Eigenvalues and eigenvectors of a 2x2 matrix (closed form) or a symmetric matrix up to 10x10 (Jacobi).

Inverse of a square matrix (up to 10x10) by Gauss-Jordan, with A*inv(A) residual and a condition number.

Least-squares line or polynomial fit (degree 1 to 6, up to 100 points) with coefficients, R-squared and residuals.

Multiply two matrices (up to 10x10) given as JSON, with shape check and the product matrix.

Rank, nullity and reduced row echelon form of a matrix (up to 10x10) with pivot columns.

Solve Ax=b (n up to 10) by Gaussian elimination with partial pivoting; flags singular and ill-conditioned systems.

Compose 2D or 3D rotate, scale and translate steps into one homogeneous matrix, optionally applied to a point.

Transpose a matrix (up to 10x10) with trace, symmetry and skew-symmetry flags, and Frobenius and 1-norms.

Vector dot, cross, norm, angle, projection, unit vector and distance for vectors of up to 100 entries.