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Eigenvalue and Eigenvector Calculator With Steps

The characteristic polynomial, its roots, and each eigenvector worked out in full.

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What this eigenvalue solver is designed for

  • Characteristic polynomials
  • Eigenvalues of 2x2 and 3x3 matrices
  • Eigenvectors and eigenspaces
  • Diagonalisation

How to use it

  1. 1Enter the matrix.
  2. 2Follow the characteristic polynomial step.
  3. 3Read each eigenvalue with its eigenvector.

Eigenvalue problems to try

eigenvalues of [[2,1],[1,2]]eigenvectors of [[4,1],[2,3]]

Eigenvalue solver FAQ

Can it diagonalise a matrix?
Yes, when the matrix has a full set of independent eigenvectors; otherwise the steps explain why it cannot.

Continue with a related solver

Matrix

Every row operation is shown so you can reproduce the reduction by hand.

Linear algebra

Structured working for the linear algebra problems that usually lose marks in the middle steps.

System of equations

Enter every equation on its own line and follow the elimination or substitution through to the solution.

Looking for the formulas instead? Browse the formula reference.