Eigenvalues and eigenvectors (eig) in SciPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is an eigenvalue in the context of a matrix?

An eigenvalue is a special number that shows how much a matrix stretches or shrinks a vector when multiplied by it. It tells us the factor by which the vector changes length.

beginner

What is an eigenvector?

An eigenvector is a vector that does not change direction when a matrix multiplies it. It may get longer or shorter, but it points the same way.

beginner

How do you compute eigenvalues and eigenvectors using scipy?

You use the function scipy.linalg.eig(matrix). It returns two arrays: one for eigenvalues and one for eigenvectors.

intermediate

Why are eigenvalues and eigenvectors important in data science?

They help us understand data patterns, reduce data size, and find directions of maximum variance, like in Principal Component Analysis (PCA).

intermediate

What does it mean if an eigenvalue is zero?

A zero eigenvalue means the matrix squashes some vectors completely to zero, showing that the matrix is not invertible and loses some information.

Which function in scipy computes eigenvalues and eigenvectors?

A scipy.linalg.solve

B scipy.linalg.inv

C scipy.linalg.det

D scipy.linalg.eig

scipy.linalg.eig is the function used to compute eigenvalues and eigenvectors.

What does an eigenvector do when multiplied by its matrix?

A Changes length but not direction

B Remains unchanged

C Changes both length and direction

D Changes direction but not length

An eigenvector keeps its direction but its length can change when multiplied by the matrix.

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

A The matrix is diagonal

B The matrix is invertible

C The matrix is singular (not invertible)

D The matrix is identity

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

Which of these is a use of eigenvalues and eigenvectors in data science?

A Sorting data alphabetically

B Reducing data dimensions with PCA

C Calculating averages

D Counting missing values

Eigenvalues and eigenvectors are used in PCA to reduce data dimensions.

What do the outputs of scipy.linalg.eig represent?

A Eigenvalues and eigenvectors

B Matrix inverse and determinant

C Matrix rank and trace

D Singular values and vectors

scipy.linalg.eig returns eigenvalues and eigenvectors of a matrix.

Explain in your own words what eigenvalues and eigenvectors are and why they matter.

Think about how a matrix changes vectors and what stays the same.

Describe how you would use scipy to find eigenvalues and eigenvectors of a matrix.

Focus on the function name and what it returns.