Eigenvalue and Eigenvector Tool

Choose a `2 Γ— 2` or `3 Γ— 3` matrix, calculate its eigenvalues, then see real eigenvectors, the transform matrix `𝒯`, and the diagonal matrix `π’Ÿ` when diagonalization is possible.

A

Results

After you calculate
This tool will show eigenvalues, eigenvectors, the transform matrix 𝒯, and the diagonal matrix π’Ÿ when the matrix can be diagonalized.

For 2Γ—2: solve det(A βˆ’ Ξ»I) = 0, then solve (A βˆ’ Ξ»I)v = 0 for each eigenvalue. If there are enough independent real eigenvectors, the tool also forms 𝒯 and π’Ÿ.