Learning Path
Question & Answer1
Understand Question2
Review Options3
Learn Explanation4
Explore TopicChoose the Best Answer
A
To simplify the matrix into orthogonal components for easier interpretation
B
To find the inverse of the matrix directly
C
To compute the determinant of the matrix
D
To combine multiple matrices into one single matrix
Understanding the Answer
Let's break down why this is correct
Answer
Singular value decomposition breaks a matrix into three parts: a left‑singular matrix, a diagonal matrix of singular values, and a right‑singular matrix. This lets us see how the matrix stretches space along orthogonal directions, with the singular values telling how much each direction is stretched. By keeping only the largest singular values, we can approximate the original matrix with fewer dimensions, which is useful for compression or noise reduction. For example, if a 3×3 image matrix has singular values 10, 2, 0. 5, we might keep only the first two to create a simpler yet close image representation.
Detailed Explanation
SVD splits a matrix into two rotations and a diagonal scaling. Other options are incorrect because SVD does not give the inverse directly; SVD is not used to compute the determinant.
Key Concepts
Matrix Decomposition
Singular Value Decomposition
Eigen Decomposition
Topic
Matrix Decomposition Techniques
Difficulty
easy level question
Cognitive Level
understand
Practice Similar Questions
Test your understanding with related questions
1
Question 1A company is analyzing customer feedback data represented as a matrix, where each row corresponds to a different customer and each column corresponds to a particular feature of the feedback. They decide to apply Singular Value Decomposition (SVD) to identify underlying patterns in the feedback. How can using SVD in this context enhance their understanding of customer preferences?
hardMathematics
Practice
2
Question 2If a matrix undergoes singular value decomposition (SVD) resulting in clearer patterns in data for machine learning applications, what underlying property of the matrix is primarily responsible for this effect?
hardMathematics
Practice
Ready to Master More Topics?
Join thousands of students using Seekh's interactive learning platform to excel in their studies with personalized practice and detailed explanations.