[Solved] Which of the following statements about the matrices U and V from [U, S, V] = svd(A); is true? — Ans: Both U and V are orthogonal matrices | MATLAB

MATLAB - Linear Algebra

Which of the following statements about the matrices U and V from [U, S, V] = svd(A); is true?

A<code>U</code> and <code>V</code> are always square identity matrices

B<code>U</code> is diagonal and <code>V</code> is upper triangular

C<code>U</code> contains eigenvalues and <code>V</code> contains eigenvectors

DBoth <code>U</code> and <code>V</code> are orthogonal matrices

Step-by-Step Solution

Solution:

Step 1: Recall properties of U and V in SVD
In singular value decomposition, U and V are orthogonal matrices, meaning their columns are orthonormal vectors.
Step 2: Confirm orthogonality
Orthogonal matrices satisfy U'*U = I and V'*V = I, where I is the identity matrix.
Final Answer:
Both U and V are orthogonal matrices -> Option D
Quick Check:
U and V are orthogonal matrices [OK]

Quick Trick: U and V are always orthogonal in SVD [OK]

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