What is the function to get both eigen values and eigen vectors of a matrix?Select one:eig[]eig()eigval()eigval[]

Break Down the Problem

1. Identify the options provided for the function that computes both eigenvalues and eigenvectors of a matrix.
2. Determine the correct syntax and function name used in popular programming libraries (such as NumPy in Python).

Relevant Concepts

1. Eigenvalues and eigenvectors are computed using specific functions in numerical libraries.
2. In Python's NumPy library, the function eig() is used to obtain both eigenvalues and eigenvectors of a square matrix.

Analysis and Detail

1. Options:

   • eig[] - This syntax is incorrect as it appears to be array indexing rather than a function call.
   • eig() - This is likely the correct function to use for obtaining eigenvalues and eigenvectors.
   • eigval() - This function typically returns only the eigenvalues, not the eigenvectors.
   • eigval[] - Similar to eig[], this is an incorrect syntax for obtaining values.

2. Function Explanation: The eig() function in NumPy returns a tuple where the first element is an array of eigenvalues and the second element is a 2D array comprising the corresponding eigenvectors.

Verify and Summarize

The most commonly used function to obtain both eigenvalues and eigenvectors in Python’s NumPy library is indeed eig().

Final Answer

The correct function to get both eigenvalues and eigenvectors of a matrix is eig().