Can I know about eigenvalue and eigenvector?

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that does not change its direction, when that linear transformation is applied to it. More formally, if T is a linear transformation from a vector space V over a field F into itself and V is a vector in V that is not the zero vector, then v is an eigenvector of T if T (v) is a scalar multiple of v. This condition can be written as the equation {\displaystyle T(\mathbf {v} )=\lambda \mathbf {v} ,} {\displaystyle T(\mathbf {v} )=\lambda \mathbf {v} ,} Where is a scalar in the field F, known as the eigenvalue, characteristic value, or characteristic root associated with the eigenvector v. If the vector space V is finite-dimensional, then the linear transformation T can be represented as a square matrix A, and the vector v by a column vector, rendering the above mapping as a matrix multiplication on the left hand side and a scaling of the column vector on the right hand side in the equation {\displaystyle A\mathbf {v} =\lambda \mathbf {v} .} {\displaystyle A\mathbf {v} =\lambda \mathbf {v} .} There is a correspondence between n by n square matrices and linear transformations from an n-dimensional vector space to itself. For this reason, it is equivalent to define eigenvalues and eigenvectors using either the language of matrices or the language of linear transformations.

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