What are eigenvalues?

Eigenvalues are scalars lambda such that det(A - lambda*I) = 0. They represent scaling factors for eigenvectors.

How to find eigenvalues?

Solve the characteristic equation det(A - lambda*I) = 0. For 2x2: lambda^2 - tr(A)*lambda + det(A) = 0.

How many eigenvalues?

An nxn matrix has n eigenvalues (counting multiplicities). They can be real or complex.

What do eigenvalues tell us?

They determine matrix behavior: stability, diagonalization, spectral decomposition.

IP331.com | Online Tools

Algebra Tools Geometry Tools Trigonometry Tools Matrix Tools Function Tools Number Theory Tools Base Converter Electronics & Physics Statistics Tools Life & Finance

Home›Matrix Tools›Eigenvalue Calculator

Eigenvalue Calculator

Find eigenvalues by solving det(A - lambda*I) = 0

Enter 2x2 Matrix

Eigenvalue Formula

det(A - lambda*I) = 0 (characteristic equation)

2x2: lambda^2 - tr(A)*lambda + det(A) = 0

Sum of eigenvalues = tr(A)

Product of eigenvalues = det(A)

Eigenvalues are fundamental to understanding linear transformations. They determine matrix diagonalization, stability, and spectral properties.

More Matrix Tools

LU Decomposition Calculator

Compute A = LU where L is lower triangular and U is upper triangular

›

Matrix Rank Calculator

Compute rank for 2x2 and 3x3 matrices via RREF

›

Unitary Matrix Checker

Verify if a matrix is unitary (U*U = UU* = I) with detailed verification

›

Matrix Logarithm Calculator

Compute log(I+A) for 2x2 matrices using Taylor series expansion

›

Inverse Matrix Calculator

Compute the inverse via adjugate method for 2x2 and 3x3

›

Adjugate Matrix Calculator

Compute adjugate via minors and cofactors for 2x2 and 3x3

›