Diagonalization

Section 7.2 Diagonalization

Let

A

be a square matrix. If you would like to know the matrix

P

and

D

such that

P^{- 1} A P = D,

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you can do it in such way.


    
        
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A = matrix(2,2,[2, -12, 1, -5]) 
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A.eigenmatrix_right()

    
    
    
    
        
            
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Let check if the columns of

P

are eigenvectors.


    
        
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D,P = A.eigenmatrix_right()
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a1, a2 = P.column(0), P.column(1)
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A*a1, A*a2

    
    
    
    
        
            
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Important: Are you able to see that

A P = P X .

Figure out the matrix

X

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Exercise: For the matrix

B = (\begin{matrix} 1 & 2 & - 2 \\ - 2 & 5 & - 2 \\ - 6 & 6 & - 3 \end{matrix}),

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find the matrix

P

and

D

such that

P^{- 1} A P = D .

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