There are many problems in finding a basis for consisting of the eigenvectors of a square matrix. These bases can be used to study the geometric properties of A and simplify various numerical calculations involving A. These bases are also important in various applications, one of which is from these bases we can derive the properties of vector spaces one of which is that each eigenspace is a subspace of its vector space. The problem of finding a basis consisting of eigenvectors is equivalent to the diagonalization problem. The author of this article will, the diagonalization of linear operators.
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