Diagonalizable matrix

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In linear algebra, a square matrix A {\displaystyle A} is called diagonalizable or non-defective if it is similar to a diagonal matrix. That is, if there exists an invertible matrix P {\displaystyle P} and a diagonal matrix D {\displaystyle D} such that P − 1 A P = D {\displaystyle P^{-1}AP=D} . This is equivalent to A = P D P − 1 {\displaystyle A=PDP^{-1}} . (Such P {\displaystyle P} , D {\displaystyle D} are not unique.) This property exists for any linear map: for a finite-dimensional vector...

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