📚 Learning Guide
Matrix Decomposition Techniques
easy

Singular Value Decomposition : Principal Component Analysis :: Eigen Decomposition : ?

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Choose the Best Answer

A

Data Compression

B

Matrix Inversion

C

Polynomial Roots

D

Linear Regression

Understanding the Answer

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Answer

Singular Value Decomposition is a general matrix factorisation that can be used to compute the principal components of a data set, so we say SVD : PCA. Likewise, the eigen decomposition of the covariance matrix gives the same principal components, so Eigen Decomposition : PCA. In practice you first compute the covariance matrix of your centred data, then find its eigenvalues and eigenvectors; the eigenvectors are the directions of maximum variance. For example, if you have a 2‑by‑2 covariance matrix [[2,1],[1,2]], its eigen decomposition gives eigenvalues 3 and 1 and eigenvectors that point along the directions of greatest and least spread, which are the principal axes.

Detailed Explanation

Singular Value Decomposition (SVD) breaks a matrix into simpler parts that reveal hidden patterns. Other options are incorrect because Some think decomposition is used for matrix inversion, but that is a separate operation; Polynomial roots are about solving equations, not breaking matrices.

Key Concepts

Matrix Decomposition Techniques
Dimensionality Reduction
Data Analysis
Topic

Matrix Decomposition Techniques

Difficulty

easy level question

Cognitive Level

understand

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