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My questions are about how $a_1$ and $q_2$ are defined.

By Gram-Schmidt, we first let $q_1 = a_1.$ Then $u_1 = \frac{q_1}{\|q_1\|}$ is the normalized version of $q_1.$ Here, $u_1 \neq a_1.$ This contradicts the linked passage above.

Also, $q_2 = a_2 - \frac{}{\|q_1\|^2}q_1$ and so $u_2 = \frac{q_2}{\|q_2\|}.$ Here, $q_2$ is different from how it's defined above and also seems like $u_2 \neq a_2.$

If I am wrong, please point out my mistakes. I am trying to see where my thinking keeps going wrong.

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    Which book is this from? Sure, the notations are unclear. For clear notations check page 310 in http://bookstore.siam.org/ot71/ – 2017-02-20
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    @ stud_iisc, It's from Kuldeep Singh's Linear Algebra. I love this book. I just think these are just a couple of typos. – 2017-02-20

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