np.linalg.eig() for eigenvalues in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does the function np.linalg.eig() compute?

It computes the eigenvalues and eigenvectors of a square matrix. Eigenvalues tell us how much the matrix stretches or shrinks vectors, and eigenvectors show the directions that stay the same after the matrix transformation.

beginner

What are eigenvalues in simple terms?

Eigenvalues are numbers that tell us how much a matrix stretches or shrinks a vector when it is multiplied by that matrix. They help us understand the matrix's behavior.

beginner

What shape must the input matrix have for np.linalg.eig() to work?

The input must be a square matrix, meaning it has the same number of rows and columns.

intermediate

What does the output of np.linalg.eig() look like?

It returns two arrays: one with eigenvalues and one with eigenvectors. The eigenvectors are columns in the second array, each matching the eigenvalue at the same position.

beginner

How can eigenvalues and eigenvectors be useful in real life?

They help in many areas like data science for reducing data size (PCA), physics for understanding vibrations, and computer graphics for transformations.

What type of matrix can you use with np.linalg.eig()?

A Square matrix

B Rectangular matrix

C Only diagonal matrix

D Only identity matrix

np.linalg.eig() requires a square matrix because eigenvalues and eigenvectors are defined only for square matrices.

What does the first output of np.linalg.eig() represent?

A Inverse matrix

B Eigenvectors

C Eigenvalues

D Determinant

The first output is an array of eigenvalues of the input matrix.

In the output of np.linalg.eig(), how are eigenvectors arranged?

A Eigenvectors are not returned

B Each eigenvector is a column in the second output array

C Eigenvectors are scalars in the first output

D Each eigenvector is a row in the first output array

Eigenvectors are returned as columns in the second output array.

Which of these is a practical use of eigenvalues and eigenvectors?

A Sorting numbers

B Counting unique values

C Calculating averages

D Data compression and feature reduction

Eigenvalues and eigenvectors are used in techniques like PCA for data compression and feature reduction.

If a matrix has an eigenvalue of zero, what does it mean?

A The matrix is singular (not invertible)

B The matrix is identity

C The matrix is diagonal

D The matrix is symmetric

An eigenvalue of zero means the matrix is singular and cannot be inverted.

Explain what np.linalg.eig() does and describe its inputs and outputs.

Think about what eigenvalues and eigenvectors mean and how they relate to the input matrix.

Describe a real-world example where eigenvalues and eigenvectors might be useful.

Consider areas where understanding directions and magnitudes of change is important.