Diagonalize Matrix Calculator
Find the diagonal form of a matrix and its corresponding eigenvectors.
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How Matrix Diagonalization Works
A matrix A is diagonalizable if there exists an invertible matrix P and a diagonal matrix D such that:
\[ A = PDP^{-1} \]
Where:
- D is the diagonal matrix containing the eigenvalues
- P is the matrix whose columns are the eigenvectors
- P⁻¹ is the inverse of P
The process involves:
- Finding the eigenvalues by solving det(A - λI) = 0
- Finding the eigenvectors for each eigenvalue
- Constructing P from the eigenvectors
- Constructing D from the eigenvalues