Скачать или смотреть Shortcut Method to Find Eigenvectors of 3 × 3 matrix | Repeated Eigenvalues | Linear Algebra

In this video we discuss a shortcut method to find eigenvectors of a 3 × 3 matrix when there are two distinct eigenvalues. You will see that you may find the eigenvectors by simply subtracting the eigenvalues by diagonal entries of the matrix. Then, the nonzero columns of the resulting matrix, that we call the Eigenmatrix, are the eigenvectors for the complementary eigenvalue.

The term Eigenmatrix is a new term introduced to the realm of mathematics, and well align with the terms eigenvalues and eigenvectors. For such matrices we use the notation κ (Greek letter kappa), since we use λ and μ for eigenvectors and ν (Nu) for eigenvectors. It is interesting to note that κ, λ, μ and ν are four consecutive letters of the Greek alphabet.

Shortcut method to find eigenvectors
2×2 matrix    • Shortcut Method to Find Eigenvectors of 2 ...  
3×3 matrix (Distinct eigenvalues)    • Shortcut Method to Find Eigenvectors of 3 ...  
3×3 matrix (Two eigenvalues)    • Shortcut Method to Find Eigenvectors of 3 ...  
3×3 matrix (Defective matrix)    • Shortcut Method to Find Eigenvectors of a ...  

Research article https://arxiv.org/abs/2002.06203

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#Eigenvalue #Eigenvector #Eigenmatrix