np.linalg.inv() for matrix inverse in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does np.linalg.inv() do in NumPy?

np.linalg.inv() calculates the inverse of a square matrix. The inverse matrix, when multiplied by the original, gives the identity matrix.

beginner

What kind of matrix can np.linalg.inv() invert?

Only square matrices (same number of rows and columns) that are non-singular (have a non-zero determinant) can be inverted using np.linalg.inv().

intermediate

What happens if you try to invert a singular matrix with np.linalg.inv()?

NumPy will raise a LinAlgError because singular matrices do not have an inverse.

beginner

How can you verify that a matrix A and its inverse A_inv are correct?

Multiply A by A_inv. The result should be the identity matrix, which has 1s on the diagonal and 0s elsewhere.

beginner

Write a simple example to compute the inverse of a 2x2 matrix using np.linalg.inv().

<pre>import numpy as np
A = np.array([[4, 7], [2, 6]])
A_inv = np.linalg.inv(A)
print(A_inv)</pre>

What type of matrix can np.linalg.inv() invert?

A Only singular matrices

B Any rectangular matrix

C Square and non-singular matrices

D Only diagonal matrices

Only square matrices with a non-zero determinant (non-singular) can be inverted.

What error does np.linalg.inv() raise if the matrix is singular?

A ValueError

B LinAlgError

C TypeError

D IndexError

NumPy raises a LinAlgError when trying to invert a singular matrix.

What is the result of multiplying a matrix by its inverse?

A Zero matrix

B Transpose matrix

C Diagonal matrix

D Identity matrix

The product of a matrix and its inverse is the identity matrix.

Which NumPy module contains the inv() function?

A numpy.linalg

B numpy.random

C numpy.fft

D numpy.core

The inv() function is in the numpy.linalg module.

What shape must a matrix have to be invertible?

A Square (same rows and columns)

B Rectangular with more rows than columns

C Rectangular with more columns than rows

D Any shape

Only square matrices can have an inverse.

Explain in your own words what np.linalg.inv() does and when you can use it.

Think about what an inverse matrix means in real life.

Describe how you would check if a matrix inverse calculation was successful using NumPy.

What is the identity matrix?