# Ruby | Matrix eigensystem() function

• Last Updated : 07 Jan, 2020

The eigensystem() is an inbuilt method in Ruby returns the Eigensystem of the matrix.

Syntax: mat1.eigensystem()

Parameters: The function does not accepts any parameter.

Return Value: It returns the Eigensystem of the matrix.

Example 1:

 `# Ruby program for eigensystem() method in Matrix`` ` `# Include matrix ``require ``"matrix"`` ` `# Initialize a matrix ``mat1 = Matrix[[``1``, ``0``], [``0``, ``2``]]       `` ` `# prints the eigensystem``puts  mat1.eigensystem()`

Output:

```Matrix[[1.0, 0.0], [0.0, 1.0]]
Matrix[[1.0, 0], [0, 2.0]]
Matrix[[1.0, 0.0], [0.0, 1.0]]
```

Example 2:

 `# Ruby program for eigensystem() method in Matrix`` ` `# Include matrix ``require ``"matrix"`` ` `# Initialize a matrix ``mat1 =  Matrix[[``1``, ``1``, ``5``], [``4``, ``1``, ``5``], [``11``, ``2``, ``12``]]        `` ` `# prints the eigensystem``puts  mat1.eigensystem()`

Output:

```Matrix[[0.3051508362231803, 0.8432205915902499, -0.04211389264475984], [0.36021591185448126, -0.07469426749056905, -1.0068644256268935], [0.881548333331269, -0.6184679554209885, 0.20869263449203795]]
Matrix[[16.624920572145022, 0, 0], [0, -2.7558784453101666, 0], [0, 0, 0.13095787316514576]]
Matrix[[0.6383015261676529, 0.14992783363808046, 0.8521544829905635], [0.9627740639327973, -0.10080816379994396, -0.2920754272026449], [0.15693539149903699, -0.9320657209209471, 0.3265344924799822]]```
My Personal Notes arrow_drop_up