Eigenvalues and eigenvectors

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In linear algebra, an eigenvector ( EYE-gən-) or characteristic vector is a (nonzero) vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector v {\displaystyle \mathbf {v} } of a linear transformation T {\displaystyle T} is scaled by a constant factor λ {\displaystyle \lambda } when the linear transformation is applied to it: ⁠ T v = λ v {\displaystyle T\mathbf {v} =\lambda \mathbf {v} } ⁠. The corresponding eigenvalue, characteristic value, or characteristic root is the multiplying factor λ {\displaystyle \lambda } (possibly a negative or complex number). Geometrically, vectors are multi-dimensional quantities with magnitude...

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