Question

We fix the dimension $n=5$. 1. For any integer $r$ between 1 and 5 , initialize (with rand) $r$ vectors $u_i$ and define a square matrix $A=\sum_{i=1}^r u_i u_i^t$. Compare the rank of $A$ with $r$. 2. Same question for vectors generated by BinChanceMat. 3. Justify your observations.

   We fix the dimension $n=5$.
1. For any integer $r$ between 1 and 5 , initialize (with rand) $r$ vectors $u_i$ and define a square matrix $A=\sum_{i=1}^r u_i u_i^t$. Compare the rank of $A$ with $r$.
2. Same question for vectors generated by BinChanceMat.
3. Justify your observations.

Numerical Linear Algebra

Grégoire Allaire,… 1st Edition

Chapter 2, Problem 6

Thanks for your feedback!

We fix the dimension $n=5$. 1. For any integer $r$ between 1 and 5 , initialize (with rand) $r$ vectors $u_i$ and define a square matrix $A=\sum_{i=1}^r u_i u_i^t$. Compare the rank of $A$ with $r$. 2. Same question for vectors generated by BinChanceMat. 3. Justify your observations.

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