If the i-th eigenvalue is real, the i-th COLUMN of the eigenvector Matrix contains the corresponding eigenvector. Also note that numbers in scientific notation are NOT recognized. In other words, this utility calculates solutions that may have imaginary components (indicated by the 'i') however, it assumes the inputs are all real (it does not accept complex inputs).ĭo not enter commas, brackets, etc. Note that the a values are assumed to be real however, the solutions may be complex. If you have all the data ready, simply enter it, click the Solve button, and it will calculate the eigenvalues of and the associated eigenvectors. To use this utility, you should have the a values ready to enter. Λ is an eigenvalue (a scalar) of the Matrix if there is a non-zero vector (v) such that the following relationship is satisfied:Įvery vector (v) satisfying this equation is called an eigenvector of belonging to the eigenvalue λ.Īs an example, in the case of a 3 X 3 Matrix and a 3-entry column vector,Īnd each eigenvector v 1, v 2, v 3, etc takes the form Please report any errors to the webmaster. These errors are mine the original FORTRAN routines have been thoroughly tested and work properly. Although all care has been taken to ensure that the sub-routines were translated accurately, some errors may have crept into the translation. The original sub-routines were written in FORTRAN and have been translated to Javascript here. 'Matrix Eigensystem Routines-(EISPACK) Guide Extension' 'Matrix Eigensystem Routines-(EISPACK) Guide' To use the utility posted on this page, please enable Javascript. The routine is written in Javascript however, your browser appears to have Javascript disabled. The algorithm is from the EISPACK collection of subroutines. This page contains a routine that numerically finds the eigenvalues and eigenvectors of a 4 X 4 Real Matrix. Eigenvalues and Eigenvectors Calculator for a 4 X 4 Real Matrix

Wolframalpha vectors