Learn to Calculate Eigenvectors and Eigenvalues by Hand - Detailed Tutorial With Example

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In this numerical linear algebra tutorial, we explain how to calculate eigenvectors and eigenvalues of matrices by hand. We first provide basic definitions of eigenvalues and eigenvectors. Then, we define the concept of a characteristic polynomial. Then, we explain how to calculate eigenvectors and eigenvalues of a 3by3 matrix completely by hand. We explained that to compute the eigenvector one needs to solve a system of linear equations that had an infinite number of solutions. That is, the systems arising from eigenvector problems are underdetermined.