Find the eigen decomposition of the matrix

Reference no: EM132662782

Mathematical Modelling and Computational Science

Exercise 1: Find, by hand, the eigen decomposition of the following matrix A:

Exercise 2: Consider the following matrix B:

1. Compute, by hand, the full SVD of the matrix B.
2. Compute, by hand, the reduced (compact) SVD of the matrix B.

Exercise 3:
The singular value decomposition is widely used in many computer science and machine learning applications. Select an application from the following and explain in details how SVD is used in this context.

• Recommender Systems
• Customer-Product purchases
• User-Song Listen Counts
• User-Movie Ratings
• Text Classification
• One Hot Encoding
• Bag of Words Counts
• TF/IDF (term frequency - inverse document frequency)
• Image Recovery
• Eigenfaces for face recognition
• Spectral Clustering -an unsupervised machine learning technique
• Background Removal from Videos

Reference no: EM132662782

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