
Understanding Singular Value Decomposition

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard

Ethan Morris
FREE Resource
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the role of matrix U in the singular value decomposition of a matrix A?
It is a matrix with random values.
It is a matrix with eigenvalues on the diagonal.
It is an orthogonal matrix with columns as unit eigenvectors of A*A^T.
It is a diagonal matrix with singular values.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following is the first step in finding the SVD of a matrix?
Find the singular values.
Calculate the determinant.
Determine matrix U.
Determine matrix V and V transpose.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you find the eigenvectors for matrix V in the SVD process?
By solving the vector equation for A and the identity matrix.
By multiplying A with its transpose.
By using random vectors.
By solving the vector equation for A^T * A and the identity matrix.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of normalizing eigenvectors in the SVD process?
To ensure they have a magnitude of one.
To make them equal to the identity matrix.
To ensure they have a magnitude of zero.
To make them orthogonal.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which eigenvalues are used to determine the singular values of a matrix?
All eigenvalues.
Only the negative eigenvalues.
Only the positive eigenvalues.
Only the zero eigenvalues.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the relationship between singular values and eigenvalues in SVD?
Singular values are the squares of the eigenvalues.
Singular values are the difference of the eigenvalues.
Singular values are the square roots of the positive eigenvalues.
Singular values are the sum of the eigenvalues.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is it important to use formulas to find matrix U in SVD?
To simplify the calculation process.
To ensure the eigenvectors are in the correct order.
To ensure the correct unit eigenvectors are used.
To avoid using the identity matrix.
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