Math calculators

Matrix calculator

Addition, multiplication, transpose, determinant, inverse, rank, trace, powers, eigenvalues and eigenvectors, and solving Ax = b.

Inputs

Results

Methodology

Conventions

  • Matrices are entered one row per line, values separated by spaces or commas, up to 6×6.
  • Determinant, inverse and solve use LU decomposition with partial pivoting; rank counts pivots above a small tolerance.
  • Eigenvalues may be complex; eigenvectors are shown only when all eigenvalues are real.

References

  • Golub and Van Loan, Matrix Computations, 4th ed. (2013)

Formulas

Product
(AB)_{ij} = \sum_k A_{ik} B_{kj}
Determinant
\det A = \det P \prod_i U_{ii}
Eigenpairs
A\mathbf{v} = \lambda \mathbf{v}