Python sympy | Matrix.diagonalize() method

With the help of sympy.Matrix().diagonalize() method, we can diagonalize a matrix. diagonalize() returns a tuple , where is diagonal 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``], ` `                                ``[``5``, ``-``2``, ``-``3``,  ``3``]]) ` ` `  `print``(``"Matrix : {} "``.``format``(M)) ` `  `  `# Use sympy.diagonalize() method  ` `P, D ``=` `M.diagonalize()   ` `     `  `print``(``"Diagonal of a matrix : {}"``.``format``(D))   `

Output:

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 sympy.diagonalize() method  ` `P, D ``=` `M.diagonalize()   ` `     `  `print``(``"Diagonal of a matrix : {}"``.``format``(D)) `

Output:

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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