Quickly diagonalize any square matrix (up to 3x3) with our free online calculator. Find eigenvalues, eigenvectors, and the resulting diagonal matrix effortlessly. Essential for linear algebra, this tool simplifies complex matrix transformations, saving you time and ensuring accuracy.
Formula:
Matrix diagonalization is the process of transforming a square matrix A into a diagonal matrix D using a similarity transformation:
A = PDP-1
Where:
- A is the original square matrix you wish to diagonalize.
- D is the resulting diagonal matrix, whose main diagonal elements are the eigenvalues (λ) of A.
- P is the invertible matrix whose columns are the corresponding eigenvectors (v) of A.
- P-1 is the inverse of matrix P.
The core concept relies on finding eigenvalues and eigenvectors that satisfy the equation Av = λv, where v is a non-zero eigenvector and λ is its corresponding eigenvalue.