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    Eigenvalue-Eigenvector

    06-27-2022 || 01:18
    Tags: #linear-algebra

    eigenvalue-eigenvector

    For any square matrix, the eigenvalue $\lambda$ and the eigenvector $\textbf{x}$ are formulated as,

    $$
    Ax = \lambda x ; x \ne 0
    $$
    Every eigenvalue $\lambda$ has a corresponding eigenvector $x$

    To find eigenvalue and vecotor we need to solve this equation with determinant,
    $$
    determinant(A - \lambda I) = 0
    $$
    That will give us the eigenvalue $\lambda$, and using those we can get the corresponding eigenvector $x$

    References