Learning Path
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Explore TopicChoose the Best Answer
A
Data Compression
B
Matrix Inversion
C
Polynomial Roots
D
Linear Regression
Understanding the Answer
Let's break down why this is correct
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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