HomeQuestionsMathematicsMatrix Decomposition Techniques
📚 Learning Guide
Matrix Decomposition Techniques
easy

True or False: Singular Value Decomposition (SVD) can be used to transform a non-square matrix into a diagonal form, thereby simplifying its analysis.

Master this concept with our detailed explanation and step-by-step learning approach

Learning Path
Learning Path

Question & Answer
1
Understand Question
2
Review Options
3
Learn Explanation
4
Explore Topic

Choose the Best Answer

A

True

B

False

Understanding the Answer

Let's break down why this is correct

Answer

True. The singular value decomposition writes any m×n matrix A as UΣVᵀ, where U and V are orthogonal and Σ is a diagonal matrix (possibly rectangular) containing the singular values. This diagonal Σ captures the essential scaling of A in orthogonal directions, so the decomposition effectively represents A in a “diagonal form” for analysis. The original matrix A itself is not diagonal, but its action is described by the diagonal Σ. For example, a 2×3 matrix [[1,0,0],[0,2,0]] has SVD with Σ=[[1,0,0],[0,2,0]], making its singular values clear.

Detailed Explanation

SVD breaks any m x n matrix into three parts: U, a diagonal matrix Σ, and V*. Other options are incorrect because The mistake is thinking only square matrices can be turned into a diagonal form.

Key Concepts

Matrix Decomposition Techniques
Singular Value Decomposition
Eigen Decomposition
Topic

Matrix Decomposition Techniques

Difficulty

easy level question

Cognitive Level

understand

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.

Start Learning with SeekhExplore More Matrix Decomposition Techniques Questions