Singular Value Decomposition (svd) in SciPy - Cheat Sheet & Quick Revision

Recall & Review

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What is Singular Value Decomposition (SVD)?

SVD is a way to break a matrix into three simpler matrices. It helps us understand the original matrix's structure and is used in data science for tasks like noise reduction and data compression.

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What are the three matrices produced by SVD?

SVD breaks a matrix into U, Σ (Sigma), and V^T. U and V^T are orthogonal matrices, and Σ is a diagonal matrix with singular values.

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How does SVD help in data science?

SVD helps reduce data size by keeping only important parts, removes noise, and finds patterns in data like images or text.

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In scipy, which function is used to perform SVD?

The function scipy.linalg.svd() is used to perform Singular Value Decomposition on a matrix.

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What does the diagonal matrix Σ represent in SVD?

Σ contains singular values that show the importance or strength of each component in the original matrix.

Which of the following is NOT a matrix output from SVD?

A U

B X

C Σ (Sigma)

D V^T

SVD outputs U, Σ, and V^T matrices. X is the original matrix, not an output.

What type of matrix is Σ in SVD?

A Diagonal matrix

B Orthogonal matrix

C Identity matrix

D Zero matrix

Σ is a diagonal matrix containing singular values.

Which scipy function performs Singular Value Decomposition?

A scipy.linalg.svd()

B scipy.linalg.eig()

C scipy.linalg.inv()

D scipy.linalg.qr()

scipy.linalg.svd() is the function for SVD.

Why is SVD useful in data science?

A To sort data alphabetically

B To encrypt data

C To increase data size

D To reduce noise and find patterns

SVD helps reduce noise and find important patterns in data.

What property do U and V^T matrices have in SVD?

A They are zero matrices

B They are diagonal

C They are orthogonal

D They are identity matrices

U and V^T are orthogonal matrices, meaning their columns are perpendicular and have length one.

Explain the three matrices produced by Singular Value Decomposition and their roles.

Think about how each matrix contributes to reconstructing the original matrix.

Describe how Singular Value Decomposition can be used to reduce noise in data.

Consider which parts of the data carry the most information.