An n*n matrix is a matrix with n rows and n columns.  

An n*n matrix is a linear transformation of n-dimensional Euclidean space. An EigenVector of an n*n matrix is a vector that gives a direction in which that transformation is simply a scaling. The amount of scaling is the associated EigenValue. This is incredibly valuable because it lets you do MatrixFactoring and MatrixAnalysis.

See also http://foldoc.org/?eigenvector

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CategoryMath