(a) Find the singular value decomposition of A. (Use a software) (b) Determine rank of A. (c) Find eigenvalues of AT A.
(a) Find the singular value decomposition of A. (Use a software) (b) Determine rank of A. (c) Find eigenvalues of AT A.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![1. Let consider the following data matrix.
\[
A = \begin{bmatrix}
0 & 1 & 3 & 1 & 0 \\
-1 & 1 & 0 & 0 & 2 \\
0 & 1 & 3 & -1 & -1 \\
2 & -1 & -1 & 2 & -2 \\
\end{bmatrix}
\]
(a) Find the singular value decomposition of \( A \). (Use a software)
(b) Determine the rank of \( A \).
(c) Find eigenvalues of \( A^\top A \).
(d) Find the orthonormal basis for \( R(A) \).
(e) Find the orthonormal basis for \( N(A) \).
(f) Find the first 2 principal components.
(g) Apply the PCA with \( k = 2 \). Plot scatter plot of the PCA result.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c9872f4-07a5-438e-9711-8d7455ed4876%2F68241339-9fa4-4637-b156-ecb2fed48f0d%2F51pqsfv_processed.png&w=3840&q=75)
Transcribed Image Text:1. Let consider the following data matrix.
\[
A = \begin{bmatrix}
0 & 1 & 3 & 1 & 0 \\
-1 & 1 & 0 & 0 & 2 \\
0 & 1 & 3 & -1 & -1 \\
2 & -1 & -1 & 2 & -2 \\
\end{bmatrix}
\]
(a) Find the singular value decomposition of \( A \). (Use a software)
(b) Determine the rank of \( A \).
(c) Find eigenvalues of \( A^\top A \).
(d) Find the orthonormal basis for \( R(A) \).
(e) Find the orthonormal basis for \( N(A) \).
(f) Find the first 2 principal components.
(g) Apply the PCA with \( k = 2 \). Plot scatter plot of the PCA result.
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