Eigenvalue and Eigenvector Calculator

Your details

Choose the dimension of the square matrix.
Row 1, column 1 entry.
Row 1, column 2 entry.
Row 2, column 1 entry.
Row 2, column 2 entry.
Eigenvalue 1 (lambda1)Diagonalizable
5

Largest real eigenvalue of the matrix.

Eigenvalue 2 (lambda2)2
Trace (sum of diagonal)7
Determinant10
Characteristic polynomiallambda^2 - 7*lambda + 10 = 0
Eigenvector 1[-0.7071, -0.7071]
Eigenvector 2[-0.4472, 0.8944]
DiagonalizableYes (distinct eigenvalues)
lambda15
lambda22
lambda3-

Largest eigenvalue: 5, smallest: 2.

  • The two eigenvalues are 5 and 2. Their sum (7) equals the trace and their product (10) equals the determinant.
  • The determinant is 10, so the matrix is invertible.

Next stepThe matrix is diagonalizable: you can write A = PDP^-1 where D is the diagonal matrix of eigenvalues and P is the matrix whose columns are the eigenvectors.

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