Diagonalize Matrix Calculator (2×2)
The Diagonalize Matrix Calculator finds the eigenvalues of a 2×2 matrix, the diagonal matrix D, and whether the matrix is diagonalizable. Enter the four entries.
Formula
A = P·D·P⁻¹ where D holds the eigenvalues on its diagonal
- A 2×2 matrix is diagonalizable if it has two distinct eigenvalues, or is already diagonal.
- A repeated eigenvalue with only one independent eigenvector is not diagonalizable.
[[2,1],[1,2]]
Inputs
- a₁₁: 2
- a₁₂: 1
- a₂₁: 1
- a₂₂: 2
Eigenvalues 3 and 1, so D = [[3,0],[0,1]] and the matrix is diagonalizable.
Frequently asked questions
When is a matrix diagonalizable?
When it has enough independent eigenvectors — for 2×2, when the two eigenvalues are distinct or it is already diagonal.