Eigenvalue Calculator
Compute the eigenvalues and eigenvectors of a real symmetric matrix using the Jacobi rotation method. Enter a square symmetric matrix (one row per line, values space-separated); the tool returns each eigenvalue with its eigenvector, sorted by magnitude, and verifies A·v = λ·v, orthonormality, and reconstruction A = V·diag·Vᵀ. Everything runs locally in your browser.
Symmetric matrix (one row per line)
Space-separated values; the matrix must be square and symmetric (A = Aᵀ).
Summary
Eigenpairs (sorted by |λ| descending)
For a symmetric matrix the eigenvalues are real and the eigenvectors are orthogonal — the Jacobi method exploits this by repeatedly applying plane rotations J(p,q,θ) that zero the largest off-diagonal element, converging to VᵀAV = diag(λ₁…λₙ). The columns of V are the eigenvectors. The sum of eigenvalues equals the trace and their product equals the determinant; both are checked here. For non-symmetric matrices eigenvalues can be complex and require a different algorithm (QR with shifts), which this tool does not attempt. Pairs with the Matrix Calculator, Linear System Solver, and Linear Programming tools. Everything runs locally — nothing leaves your browser.