# Eigenvalue Calculator

> Find the eigenvalues of a 2x2 matrix using trace and determinant. Returns the characteristic polynomial, discriminant, and real or complex eigenvalues from λ² − tr(A)·λ + det(A) = 0.

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

## Quick Answer

Calculate eigenvalues and eigenvectors of a square matrix. Enter the matrix elements to find characteristic polynomials and unique vector solutions.

## Definition

An eigenvalue calculator is a linear algebra tool that computes the eigenvalues and eigenvectors of a square matrix. The calculator solves the characteristic equation, defined as the determinant of the matrix minus lambda times the identity matrix equals zero, to find the eigenvalues. It then calculates the corresponding eigenspaces and eigenvectors by solving the resulting null spaces. The calculator supports matrices up to size three-by-three and outputs step-by-step determinant expansion. College math and engineering students use this tool to study linear transformations.

## How to Use

1. **Select matrix size** — Choose the dimensions of your square matrix, such as two-by-two or three-by-three.
2. **Input matrix coefficients** — Type the numerical values for each element of the matrix in the grid.
3. **Read eigenvalues and vectors** — View the calculated eigenvalues, characteristic polynomial, and corresponding 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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