# Eigenvector Calculator

> Find eigenvalues and unit eigenvectors of a 2×2 matrix. Returns trace, determinant, discriminant, both eigenvalues, and the corresponding unit eigenvectors.

**URL:** https://www.calculatoranswers.com/eigenvector-calculator
**Category:** Education

## Quick Answer

Find the eigenvalues and eigenvectors of a 2x2 or 3x3 matrix. Enter the matrix coefficients to see step-by-step algebraic calculations.

## Definition

An eigenvector calculator is a linear algebra tool that computes the eigenvalues and corresponding eigenvectors of a square matrix. Eigenvectors are non-zero vectors that change only by a scalar factor (the eigenvalue) when a linear transformation is applied to them. The calculator solves the characteristic equation det(A - λI) = 0 to find eigenvalues, and then computes the null space for each eigenvalue to resolve the eigenvectors. Computer scientists, engineers, and mathematicians use this calculator to solve systems of differential equations, perform principal component analysis, and analyze stability in physics models.

## How to Use

1. **Set matrix dimensions** — Choose the size of your square matrix, typically 2x2 or 3x3.
2. **Input matrix coefficients** — Type the numerical values into the grid cells of the matrix.
3. **Read the eigenvectors** — View the calculated eigenvalues, their algebraic multiplicities, and the corresponding normalized eigenvectors.

## Disclaimer

This calculator provides estimates for educational and planning purposes. Always consult a qualified professional for specific advice on financial, medical, legal, or other regulated decisions.

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