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# Python sympy | Matrix.diagonalize () method

Using the sympy.Matrix () method. Diagonalize () we can diagonalize the matrix.  diagonalize () returns a tuple , where diagonally and ,

Syntax: Matrix (). Diagonalize ()

Returns: Returns a tuple of matrix where the second element represents the diagonal of the matrix.

Example # 1:

 ` # import sympy ` ` from ` ` sympy ` ` import ` ` * ` ` M ` ` = ` ` Matrix ([[` ` 3 ` `, ` ` - 2 ,  4 , - 2 ], `` [ 5 ,  3 , - 3 , - 2 ],   [ 5 , - 2 ,  2 , - 2 ],   [< / code> 5 , - 2 , - 3 ,  3 ]])    print ( "Matrix: { } " . format (M))   # Use the sympy.diagonalize () method P, D = M.diagonalize ()    print ( "Diagonal of a matrix: {}" . format (D)) `

Exit:

Matrix: Matrix ([[3, -2, 4, -2], [5, 3, -3, -2], [5, -2, 2, -2], [5, -2, -3, 3]])
Diagonal of a matrix: Matrix ([[- 2, 0, 0, 0], [0, 3, 0, 0], [0, 0, 5, 0], [0, 0, 0, 5]])

Example # 2:

 ` # import sympy ` ` from ` ` sympy ` ` import ` ` * ` ` M ` ` = ` ` Matrix ([[` ` 1 ` `, ` ` - ` ` 3 ` `, ` ` 3 ` `], [` ` 3 ` , ` - ` ` 5 ` `, ` ` 3 ` `], [` ` 6 ` ` , ` ` - ` ` 6 ` `, ` ` 4 ` `]]) ` ` print ` ` (` ` "Matrix: {}" ` `. ` ` format ` ` (M)) `   ` # Use the method sympy.diagonalize () ` ` P, D ` ` = ` ` M.diagonalize () ` ` `  ` print ` ` (` ` "Diagonal of a matrix: {}" ` `. ` ` format ` ` (D)) `

Exit:

Matrix: Matrix ([[1 , -3, 3], [3, -5, 3], [6, -6, 4]])
Diagonal of a matrix: Matrix ([[- 2, 0, 0], [0, -2, 0], [0, 0, 4]])

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