# Diagnolize Calculator 2×2 Matrix

# 2×2 Matrix Diagonalization Calculator

Your eigen vector may differ slightly

## What is Matrix Diagonalization?

Matrix diagonalization is the process of converting a square matrix into a diagonal matrix. Diagonal matrices have non-zero entries only on the main diagonal, with all other entries being zero.

## Steps to Diagonalize a Matrix:

- Find the eigenvalues of the matrix.
- Find the corresponding eigenvectors for each eigenvalue.
- Construct the matrix of eigenvectors and its inverse.
- Form the diagonal matrix using the eigenvalues.
- Verify the diagonalization by computing \( P^{-1}AP \), where \( P \) is the matrix of eigenvectors.

## FAQs

## What are eigenvalues and eigenvectors?

Eigenvalues and eigenvectors are concepts in linear algebra. Given a square matrix, an eigenvalue is a scalar that represents how the matrix stretches or shrinks a corresponding eigenvector.

## When can a matrix be diagonalized?

A square matrix can be diagonalized if it has \( n \) linearly independent eigenvectors, where \( n \) is the size of the matrix.

## What if a matrix has complex eigenvalues?

If a matrix has complex eigenvalues, it cannot be diagonalized using real numbers. However, it can still be diagonalized using complex numbers.