## SOIDERGI

### Vector Collection Storage     # Eigenvectors Square Matrix Non Zero Vectors V Av Av Scalar Called Eigenvalue Example Q

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Define an eigenvalue to be any scalar K such that there exists a non-zero vector v V satisfying Equation . It is important that this version of the definition of an eigenvalue specify that the vector be non-zero otherwise by this definition the zero vector would allow any scalar in K to be an eigenvalue.Non-square matrices do not have eigenvalues. If the matrix X is a real matrix the eigenvalues will either be all real or else there will be If 0 were allowed as an eigenvector suddenly every lambda in mathbb R would be an eigenvalue for it rendering PCA meaningless because under its interpretation of the covariance eigenvectors there would now be a pringraphicl component (the zero vector) with undefined variance attached.

Specifically we are interested in those vectors v for which Avkv where A is a square matrix and k is a real number. A vector v for which this equation hold is called an eigenvector of the matrix A and the graphicociated constant k is called the eigenvalue (or characteristic value) of the vector v.Feb 14 2011 Is there such a thing as a square matrix with no eigenvectors Av v for any (non-zero) vector v. not simple scalar multiplications. Eigen vectors Oct 23 2012 Suppose a square matrix A superset of the set of eigenvectors corresponding to zero eigenvalue there exists a non-zero vector v such that [itex]Av