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Matrix diagonalization

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Definition of matrix diagonalization
Definition of diagonalizable matrix
An n-by-n matrix is diagonalizable if and only if it has n linearly independent eigenvectors.
An n-by-n matrix is diagonalizable if and only if the sum of the dimensions of the eigenspaces equals n.
Diagonalizability requires splitting and equality of geometric and algebraic multiplicities
A diagonalizable matrix is diagonalized by a matrix having the eigenvectors as columns.
An n-by-n matrix is diagonalizable if and only if the union of the basis vectors for the eigenspaces is a basis for R^n (or C^n).
An n-by-n matrix with n distinct eigenvalues is diagonalizable.
Real block form and complex diagonalization for a 2-by-2 matrix

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A diagonalizable matrix is diagonalized by a matrix having the eigenvectors as columns.

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