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Memory Based GATE DA 2024 | Question: 29

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Consider the vector \( u = \begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \\ 5 \end{bmatrix} \), and let \( M = uu^{\top} \). If \( \sigma_1, \sigma_2, \sigma_3, \ldots, \sigma_5 \) are the singular values of \( M \), what is the value of \( \sum_{i=1}^5 \sigma_i \)?
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The u is given as u = [1 2 3 4 5 ]T.   [...]T  is used to represent a column vector.

M = uuT = [1 2 3 4 5 ]T [1 2 3 4 5] = 

    

So the sum of singular values,  the sum of the diagonal elements = 1+4+9+16+25 = 55. 

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