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A diagonal matrix is a square matrix whose only non zero entries are on the diagonal, i.e.
diagonal if, and only if,
If the diagonal entries are
is a diagonal matrix.
A square matrix A is diagonalizable if there exists an invertible matrix P such that P-1AP is a
Consider the square matrix A
of order n
as the matrix of an endomorphism of
standard basis. If there exist a basis of
composed only from eigenvectors of A
, then A
The matrix P is the change of base matrix from the standard basis to the basis of eigenvectors.
With the settings of 4.3
, we have the eigenvectors
They are linearly independent; as
they form a basis of V
. Define the matrix